Use trigonometric identities to verify each expression is equal. csc2(x) - 2csc(x)cot(x) + cot2(x) = tan2(x/2)

Answers

Answer 1

By definition of csc and cot,

csc²(x) - 2 csc(x) cot(x) + cot²(x) = …

… = 1/sin²(x) - 2 cos(x) / sin²(x) + cos²(x) / sin²(x)

Combining fractions,

… = (1 - 2 cos(x) + cos²(x)) / sin²(x)

Factorize the numerator and use the Pythagorean identity,

cos²(x) + sin²(x) = 1,

to rewrite the denominator.

… = (1 - cos(x))² / (1 - cos²(x))

Cancel a factor of 1 - cos(x).

… = (1 - cos(x)) / (1 + cos(x))

Using the half-angle identities,

sin²(x) = (1 - cos(2x))/2

cos²(x) = (1 + cos(2x))/2

it follows that

1 - cos(x) = 2 sin²(x/2)

1 + cos(x) = 2 cos²(x/2)

and so

… = (2 sin²(x/2)) / (2 cos²(x/2))

… = sin²(x/2) / cos²(x/2)

Finally, by definition of tangent,

… = tan²(x/2)


Related Questions

Which of the following statements about the administration of cpr is true?.

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Explanation:

hope this will helps you

Which of the following best describes the meaning of "force"?.

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Answer:no no no no no no

Explanation: yes yes yes yes yes

Which characteristics describe most nonmetals in the solid phase.

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Solid nonmetals are generally brittle, with little or no metallic luster. Most nonmetals have the ability to gain electrons easily. Nonmetals display a wide range of chemical properties and reactivities.

If you have a choice to earn simple interest on $10,000 for three years at 8% or annually compounded interest at 7. 5% for three years which one will pay more and by how much?.

Answers

Answer:

annually compounded interest at 7. 5% for three years will pay more by $22.97

Explanation:

Simple interest

A = P (1+ rt)

A = final amount

P = initial principal balance

r = interest rate

t = number of time periods elapsed

A = 10000(1+0.08x3) = $12,400

Annual compound interest

A = P (1+ r/n)^nt

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

A = 10000(1+0.075/1)^(1x3) = $12,422.97

$12,422.97 - $12,400 = $22.97

The aachen gospels of otto the third manuscript. Christ is washing his apostles feet in front of a large building. The aachen gospels of otto iii, part of which is shown above, is an example of what kind of manuscript?.

Answers

Answer:

It is an Ottonian manuscript. It produced magnificent medieval illuminated manuscripts and it is about religion. They were a major art form of the time, and monasteries received direct sponsorship from emperors and bishops, having the best in equipment and talent available. The range of heavily illuminated texts was very largely restricted (unlike in the Carolingian Renaissance) to the main liturgical books, with very few secular works being so treated.

Explanation:

Answer:

An Ottonian manuscript.

Explanation:

Edge 2022

Which of the following graphs could be the graph of the function f(x) = x3 + 8? mc019-1. Jpg mc019-2. Jpg mc019-3. Jpg mc019-4. Jpg.

Answers

Functions can be represented using equations, graphs and tables.

The graphs are not given.

So, we simply plot the graph of the given function.

The function is given as:

[tex]f(x) = x^3 + 8[/tex]

When x = 1, we have:

[tex]f(1) = 1^3 + 8[/tex]

[tex]f(1) = 9[/tex]

When x = 2, we have:

[tex]f(2) = 2^3 + 8[/tex]

[tex]f(2) = 16[/tex]

When x = 3, we have:

[tex]f(3) = 3^3 + 8[/tex]

[tex]f(3) = 35[/tex]

When x = 4, we have:

[tex]f(4) = 4^3 + 8[/tex]

[tex]f(4) = 72[/tex]

Represent the above results as a table, we have:

x          f(x)

1          9

2         16

3          35

4          72

See attachment for the table of [tex]f(x) = x^3 + 8[/tex]

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Which of these contributed the most to the florida land boom.

Answers

Answer:

Florida land boom which was in the year 1920 was termed as the first real estate bubble which was in the Florida.

This bubble busted which left back remains of failed development projects and new cities for example, Aladdin city which is in the southern part of Miami-dade country and Miami Isola di Lolando.

The result of Florida's land boom created many cities out of Everglades and shaped Florida for many years.

During that time of land boom the prices on speculation were raised and development and land boom ensued.

Explanation:

Answer:

It is B they were able to travel to Florida for the land

Explanation:

The quote below was written in the 1920s: the disaster which was impending was destined to be as bewildering and frightening to the rich and the powerful and the customarily sagacious as to the foolish and unwary holder of fifty shares of margin stock. --frederick lewis allen source: http://xroads. Virginia. Edu/~hyper/allen/ch13. Html to what event does this quote refer? the events on black tuesday the programs of the first new deal the dust bowl the end of the dust bowl.

Answers

Answer:A the events of black teusday

Explanation:

Answer:

I think that it's c: the dust bowl

Explanation:

What would happen to crabtree if he was ever late to work? he would lose his wages. He would get in trouble with his parents. He would be beaten. He would be fired.

Answers

Answer:

he would be beaten

Explanation:

He would be beaten if he was ever late to work. Therefore option C is correct.

What are Parents?

It would seem simple to define the term "parenting" as follows: Parenting is the act of nurturing, supporting, encouraging, directing, guiding, and loving a child or children from infancy to adulthood.

Consistency and routine are key components of good parenting, which provides kids with a sense of control. Redundancy becomes the goal for parents because good parenting emphasizes helping children become independent. A style of parenting that takes into account the age and developmental stage of the kid is good parenting.

The biological parents of a kid are typically the father and mother whose DNA the child carries. Although they do not need to be blood relatives, legal parents have a family link to the kid by law, such as in the case of an adopted child.

Hence, He would be beaten if he was ever late to work.

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Why there's no place like home for the holidays commonlit answers.

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People often looks forward to holidays. Why there's no place like home for the holidays is due to different reasons such as;

Christmas rituals where everyone come together and have a nice time.The home serves as an anchor of order and comfort.The home is  safe, warm and a comforting place to be.

Why there's no place like home for the holidays  is a very significant and important text by Frank T. McAndrew. This was written in 2017 to show the significance of the home. The physical surrounding often influences a man's life.

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Factual information can be presented with bias. Please select the best answer from the choices provided t f.

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Answer:

False

Explanation:

When giving factual information it is important to be able to present your views without bias. When receiving the information it is important to be able to distinguish bias from fact.

Answer:

right

Explanation:

Which of the following best describes the maya civilization?.

Answers

Answer:

It is connected directly to the Mayan government.

Explanation:

The Mayan religion was a polytheistic religion. Religious leaders were at the top of their social hierarchy. They had many rituals to honor and worship their ancestors as they believed they were the ones who interceded for the living ones.

Completa en tu cuaderno la siguiente rutina de pensamiento sobre la importancia de la nutrición.

Answers

Una nutrición balanceada es fundamental para mantener un estado saludable. Dicha nutrición se puede lograr incorporando macronutrientes y micronutrientes en cantidades adecuadas.

La nutrición se refiere al acto de ingerir alimentos para mantenerse en un estado saludable tanto físico como mental (y emocional).

Una alimentación saludable comprende la ingesta de macronutrientes, es decir, proteínas, lípidos, y carbohidratos, como así también micronutrientes tales como vitaminas y minerales.

Cada uno de estos nutrientes debe ser ingerido en cantidades adecuadas de acuerdo a las características fisiológicas del individuo, es decir, de acuerdo a su peso, edad, altura, etc.

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According to research by fergus i. M. Craik and endel tulving on levels of processing, which of the following would most improve the ability to recall the word "umbrella"?.

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According to the levels of processing, deciding whether an umbrella would be useful to pack for a trip, would most improve the ability to recall the word "umbrella". This model focuses on the depth of processing in memory.

The 'levels of processing' is a model developed by the cognitive psychologists F. Craik and R. Lockhart in 1972.

This model (levels of processing model) puts focus on the depth of processing developed for memory tasks.

This model can be used to predict how information is processed, where memory can be considered as an outcome of processing information.

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The key financial consideration in choosing between private and 3pl distribution options is.

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A key (important) financial consideration that must be considered when choosing between private and third-party logistic provider (3PL) distribution options is: the volume (quantity) of product being moved.

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Generally, there are different types of service providers in the supply and logistics chain management and they include:

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Which of the following scales is the key of c major.

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There are different scales in music. The C major (or the key of C) is known to be a major scale that is often based on C. It is made up of different pitches C, D, E, F, G, A, and B.

C major is simply known to be one of the most user key signatures found in music. It is known to have its key signature to have no flats and no sharps keys.

The C major scale is known to have the scale of zero sharps or flats. It does not have any key signature and it makes it easier to identify any music in the key of C major.

For one to be able to play the C major scale ascending, one must start with the root note C and play the notes in order: C - D - E - F - G - A - B - C. Then, one can either go right back down the scale of B - A - G- F- E - D.

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What type of fallacy does this argument represent? hasty generalization ad populum begging the claim genetic fallacy.

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Answer:

The answer is A: hasty generalization

Explanation:

Got 100% on the quiz

Answer:

A

Explanation:

Among the top motivators driving corporations to engage in csr include all of the following reasons except.

Answers

There are different types of motivating factors. Among the top motivators driving corporations to engage in CSR include all of the following reasons except Meeting or exceeding budget.

Budget meetings is simply known as a vital  meeting mainly for smaller businesses and large corporations.

These meetings are mostly held so as to talk about budget planning, the operating of budget and the various changes need to be made to the budget so as to achieve organization's goal.

There are different motivating factors aimed at increasing shareholder value and reputation management through the means of CSR reporting. Values-driven factors are known to be the most important motivators.

See full question below.

Among the top motivators driving corporations to engage in CSR include all of the following reasons EXCEPT:

Select one:

a. Meeting or exceeding budget

b. Ethical considerations

c. Innovation and learning

d. Employee motivation

a. Meeting or exceeding budget

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How can you protect yourself from internet hoaxes cyber awareness 2022.

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There are a lot of fraudulent activates on online and it is very important to guide against them. There are strategies and online resources to help you identify and respond to a potential hoax.

First Identify that it is a hoax, Note that Hoaxes often booms where they are spread quickly and without consideration. If you notice or come in contact with a hoax through social media, the right thing to do thing to do is wait. The police or the school one is attending should issue a warning on the story.

Hoaxes are very common in the internet. Even with the recent digital technology, social media etc, a lot of spread of misinformation is now been spread at a faster and broader rate.

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Where would you go to find all the lists you can use to fill in forms in quickbooks online?.

Answers

Answer:

O Go to the Gear icon select All Lists O Go to the Plus icon and choose All Lists O Go to the Accounting screen and select All Lists O Go to the Reports screen and select All Lists

Explanation:

Hope this helps!!

Itz Deepika Here to help ~

Note:- If you have any more questions then let me know .

Homework = Use Comment section

akao wrote an opinion piece about why he thinks sandwiches are the perfect food. Read the first body paragraph.

Sandwiches make healthy food taste good. You can choose a soft whole grain bread as a base. Then you can add a lean meat or some other protein, like hummus. Finally, some lettuce or other greens will give it a nice, healthy crunch.

Which sentence states the reason for Takao’s opinion?
A. "Sandwiches can be tasty and healthy too."
B. "You can choose a soft whole grain bread as a base."
C. "Then you can add a lean meat or some other protein, like hummus.
D. "Finally, some lettuce or other greens will give it a nice, healthy crunch."

Answers

Answer:

A

Not confident about this answer, so sorry if it is wrong

Explanation:

I think it is a because

It is the topic sentence

The sentence is also the only sentence to entirely be an opinion

The rest of the paragraph is talking about what you can put on it to make it taste good and be healthy

It is estimated that __________ percent of adults in the united states have a cell phone.

Answers

Cellphone consumption in the United States is such that the percentage of adults with a cell phone is 90%.

Cellphone ownership in the United StatesMore than 90% of its citizens owning a cell phone. More than 200 million adults owning a smartphone.

The United States therefore has one of the highest adult cellphone ownership rates in the world which is made easier by the packages offered by cellphone companies and networks.

In conclusion, 90% of American adults own a cell phone.

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A person is watching a boat from the top of a lighthouse.

Answers

Answer:

no way!!!!!!!!!!!!!!!!!

Explanation:

(mc)for which of the following strategic reasons did the united states acquire the midway islands? to spread christian and democratic ideals to the citizens living in the south pacific to build naval protection against rivals as the united states increased trade with asia and latin america to increase overseas trade to keep the country’s economy strong following a severe depression to slow the spread of asian countries’ influence in the pacific islands.

Answers

The reason the United States acquired the Midway Islands was to build naval protection against rivals as the United States increased trade with Asia and Latin America.

The Midway Islands:

Were the first territories in the Pacific that the U.S. acquired. Came under the administration of the U.S. Navy.

With the U.S. Navy controlling the islands, we can therefore say that the U.S. acquired the islands as a means of navy protection for American trade in Asia and related areas.

In conclusion, option B is correct.

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Answer:

to build naval protection against rivals as the United States increased trade with Asia and Latin America

Explanation:

I got it right on the test.

Eight less than four times a number is less than 56.

Answers

Answer:

depending on the number I think I could be wrong not 100%

The perimeter of the figure below is 133.1 ft.
Find the length of the missing side.

Answers

Answer:

9.6

Explanation:

because if we did if we subtract the total number which is which we are giving 133.1 minus the total number is that the Debt term give us by him by the drawing it will give us 9.6 feet

9.6 ft because if you add all the sides then subtract by the actual perimeter then you get x= 9.6 ft

What caused the february revolution of 1917 brainly.

Answers

Answer:

Russia disastrous involvement in world war l

This is the immediate cause of the February Revolution

there are 80 students in a school every student is taking either algebra or pre calculus

Answers

Answer:

Is that Real or a question

tell me pls

An event with a probability of 0 is an event with a probability of 1 is.

Answers

Answer:

An event with a probability of 0 is Impossible. ✔

An event with a probability of 1 is Certain. ✔

Hope I have  Helped ❤

How does frankenstein feel about his creation brainly.

Answers

I would say, he was pretty dang happy! Let me tell you, juggling kids, work and school! It’s crazy but this app helps me so much with my math. I really do appreciate how it explains the answer. Thank you!!
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