Verify the following identity and show steps

(Cos2 θ)/(1+sin2 θ)= (cot θ-1)/(cot θ+1)

Answers

Answer 1

Answer:

Verified below

Step-by-step explanation:

We want to show that (Cos2θ)/(1 + sin2θ) = (cot θ - 1)/(cot θ + 1)

In trigonometric identities;

Cot θ = cos θ/sin θ

Thus;

(cot θ - 1)/(cot θ + 1) gives;

((cos θ/sin θ) - 1)/((cos θ/sin θ) + 1)

Simplifying numerator and denominator gives;

((cos θ - sin θ)/sin θ)/((cos θ + sin θ)/sin θ)

This reduces to;

>> (cos θ - sin θ)/(cos θ + sin θ)

Multiply top and bottom by ((cos θ + sin θ) to get;

>> (cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ)

In trigonometric identities, we know that;

cos 2θ = (cos² θ - sin²θ)

cos²θ + sin²θ = 1

sin 2θ = 2sinθcosθ

Thus;

(cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ) gives us:

>> cos 2θ/(1 + sin 2θ)

This is equal to the left hand side.

Thus, it is verified.


Related Questions

what is the markup percentage based on retail for an item with a dollar mark up of $70.00, cost of $30.00, and retail price of $100.00?

Answers

Answer:

70/100= 0.7= 70%

70%

Solve the following word problem by creating and solving a system of linear equations. Rachel offers to go to the coffee shop to buy cappuccinos and lattes for her co-workers. She buys a total of nine drinks for $35.75. If cappuccinos cost $3.75 each and the lattes cost $4.25 each, how many of each drink did she buy? a 2 cappuccinos, 7 lattes b 6 cappuccinos, 3 lattes C 4 cappuccinos, 8 lattes d 5 cappuccinos, 4 lattes​

Answers

Answer:

85

Step-by-step explanation:


if x=49 and y=160 then what is the value of z?

Answers

9514 1404 393

Answer:

  z = 62°

Step-by-step explanation:

You know that ...

  x = (1/2)(y -z)

So ...

  2x = y - z

  z = y - 2x = 160 -2(49)

  z = 62 . . . . degrees

please help im stuck on this​

Answers

The slope of this graph is -8/5

Answer:

Slope = -8/5

Step-by-step explanation:

Use the slope formula:

m = y2 - y1 / x2 - x1

Plug in the numbers from the ordered pairs given in the graph: (-1, 4) and (4, -4).

m = -4 - 4 / 4 - - 1

m = -8 / 5

m = -8/5

m = rise/run, meaning verticl units/horizontal units

Check your work by counting it out on the graph:

From the first black dot at (-1, 4), count 8 units down and then 5 units to the right. After counting, I ended at the second ordered pair at (4, -4) which means my slope is correct.

HELP GIVING 20 POINTS
While on vacation in Belmont, Lara went out for a dinner that cost $75. If sales tax in Belmont is 8% and Lara left a 20% tip on $75, what was the total cost of her meal?

Answers

Answer:

The total cost as $96

Step-by-step explanation:

To find the total amount find the tax amount and the tip amount

75 * 8% = 6

75 * 20% = 15

add 6 and 15 to 75 to get 96

Answer:

ok

Step-by-step

ok

What is the are of the triangle?

Answers

Answer:

48 units²

Step-by-step explanation:

Area=1/2 box=hight

area=1/2×12×8

area=48

hope it helps

have a great day

Answer:

48

Step-by-step explanation:

Helppp plssssssssssss

Answers

Answer:

The answer is C

Step-by-step explanation:

If you plot them carefully.

if the sphere shown above has a radius of 15 units , then what is the volume of the sphere ?

Answers

Answer:

4,500 cubic units

Step-by-step explanation:

Answer:

4,500 cubic units

Have a good day.

Someone please answer this

Answers

Answer:

8 m is the answer.

Step-by-step explanation:

a = ?

b (Brennan and Hannah) = 6 m

c (Jayce and Hannah) = 10 m

According to the Pythagoras theorem,

a² + b² = c²

a² + 6² = 10²

a² + 36 = 100

a² = 100 - 36

a² = 64

a = 8 m

∴ Jayce and Brennan are 8 m apart.

2(x+50)=16+4x
What is x?

Answers

2x +100=16+4x
-2x. -2x
100=16+2x
-16. -16
84=2x
divide both sides
x=42

Answer:

x=42

Step-by-step explanation:

Write the equation.

2(x+50)=16+4x

Spread the parentheses

2x+100=16+4x

Put variables on one side, numbers on the other.

2x-4x=16-100

Add/subtract/multiply/divide the variables with variables and numbers with numbers.

-2x=-84

Make x alone

-x=-42

Flip sides to make x positive

42=x

Select the statement that describes this expression: 5 x 3 − (2 x 4) + 5. (2 points)

a
5 more than 3 subtract the product of 2 and 4 plus 5

b
5 times the product of 2 and 4 times 3, then add 5

c
Subtract the product of 2 and 4 from the product of 5 and 3, then add 5

d
5 more than the product of 5 and 3 plus the 2 times 4

Answers

Answer:

I believe the answer is either going to be B or C

Step-by-step explanation:

Answer:

obviously C: Subtract the product of 2 and 4 from the product of 5 and 3, then add 5

Step-by-step explanation:

plz mark as brainliest!

jack surveyed students at his school about whether they use computers or cell phones more. He found that of the 74 seventh-graders he surveyed, 53 said they used their cell phones more. In the 8th grade, 59 students used their cell phone more, compared to 38 who used their computer more. What number should be placed in the orange box below?

Answers

Answer:

Number of student of 7th grade using computer  = 21

Total number of 8th grader student surveyed  =  97

Step-by-step explanation:

The complete question is attached herewith

Solution

As we can see in the table

Total number of 7th grader student = 74

Out of these 74 student, 53 use cell phone

Hence, the number of student of 7th grade using computer = 74-53 = 21

Like wise, total number of 8th grader student surveyed = 59 +38 =  97

$410 is invested in an account earning 4.2% interest (APR), compound quarterly. Write a function showing the value of the account after t years, where the annual growth rate can be found from constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.

Answers

Report this clown who put the first answer he’s trying to get your ip

y is directly proportional to the square root of (x+2). when x =7 y=2. find y when x =98

Answers

Answer:

98/7=14

14*2=28

y=28

Step-by-step explanation:

Find the missing side length, 28,25 and x

Answers

Answer:

x

Step-by-step explanation:

Do you think the answer is A, B, C, or D.

Answers

Answer:

its A i guess

the correct answer is D

(07.01)
What is the value of x in the equation x + 10 = 13? (4 points)
1-3
0 2 3
3) 13
4) 23

Answers

x+10=13
-10 -10
—————
x= 3

Answer is: 2) 3

Answer:

x=3

Step-by-step explanation:

x+10=13

x=13-10

x=3

someone actually help me please :/ I REALLY NEED HELP AND NO ONES HELPING

Answers

Answer:

a) 8 m  

Step-by-step explanation:

a) all sides of a square are equal - there's 4 sides.

4x = 32m

x = 32/4

x = 8 m

i like ur toga pfp besty :)

The probability of event A is 0.42, and the probability of event B is 0.39. If A and B are independent events, what is P(A and B)?​

Answers

Answer:

0.1638

Step-by-step explanation:

P(A and B) or simply the probability of both events happening is the product of their individual probabilities.

P(A and B)= (0.42×0.39)= 0.1638

Find the value of x in each figure

Answers

Answer:

Value of variable 'x' is 18.

Step-by-step explanation:

From the picture attached,

In right triangle XYZ,

m(∠YXZ) = (3x + 11)°

m(∠XYZ) = 90°

m(∠XZY) = 25°

By applying triangle sum theorem in the given triangle,

m(∠YXZ) + m(XZY) + m(∠XYZ) = 180°

(3x + 11)° + (25)° + (90)° = 180°

3x + 126 = 180

3x = 54

x = 18

Therefore, value of variable 'x' is 18.

Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. If the system has one solution, find the solution.
-4x+y=12
-8x+2y=14

Answers

Answer:

no solution

Step-by-step explanation:

Classify the polyhedron. select all that apply-
•non-convex
•non-regular
•convex
•regular

Answers

convex

non-convex

regular

non-regular

Please you guys I need help!!!! I'll mark branliest !!!!


1. In triangle ABC, Angle A = 2X + 7, Angle B = 5X-15, and Angle C = 6X. What is the value of X and what are the measures of angles A,B, and C?


2. In a triangle XYZ, Angle X= 37 degrees, Angle Y = 45 degrees and Angle Z = 3x + 6. What is the value of X and what is the measure of Angle Z?

Answers

1.) 14.5
2.) X is 30.7 and Z is 98
Look at the uploaded pictures for work.

Joseph drove to his grandmother's house which is 279 miles away in 4.5 hours. If he continues at the same speed, approximately how long will it take him to drive 325 miles?

Answers

Answer:

5.24 hours

Step-by-step explanation:

I like to set these up as ratios.

279 miles/4.5 hours = 325 miles/ x hours

Then cross multiply

279x = 4.5 x 325

279x = 1462.5

divide both sides by 279

x = 5.24 hours

You can also solve 279 miles/4.5 hours to get the miles per hour driven, then divide 325 by that number:

279/4.5 = 62mph

325/62 = 5.24

Which expression is equivalent to 5 (4x+3)-2

Answers

Simplifying Expressions

To simplify an expression means to write it in the simplest way possible. Ideally, there would be no parentheses and everything has been 'expanded'.

Solving the Question

We're given:

[tex]5 (4x+3)-2[/tex]

[tex]5 (4x+3)-2[/tex]

Open up the parentheses by multiplying each term by 5:

[tex]=5*4x+5*3-2\\=20x+15-2\\=20x+13[/tex]

Answer

[tex]20x+13[/tex]

4n = 2n+6 I really need help

Answers

the answer is n=3. 4 also has a variable in front of it so (4n) which shows you have to multiply. 2 + 6 give you 8 but 2x3+6 gives you 12, 4 x 3 also gives you twelve so your answer is n=3

Plsss help mark brainlist

Answers

Answer:

17

Step-by-step explanation:

34 / 2 = 17

The perimeter of an isosceles triangle is 45 feet. The length of the shortest side is 11 feet. Find the length of the other two sides (in feet)

Answers

9514 1404 393

Answer:

  17 feet

Step-by-step explanation:

The sum of the three side lengths is the perimeter.

  s + s + 11 = 45

  2s = 34 . . . . . . subtract 11

  s = 17 . . . . . . . . divide by 2

Each of the other two sides is 17 feet.

Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.

Answers

Answer:

r = 19.0

s = 17.7

Step-by-step explanation:

In the given right triangle ABC,

Measure of Hypotenuse (AC) = 26

m(∠CAB) = 43°

By applying sine rule in the given triangle,

sin(43)° = [tex]\frac{\text{Opposite side}}{Hypotenuse}= \frac{BC}{AC}[/tex]

sin(43)° = [tex]\frac{s}{26}[/tex]

s = 26[sin(43)°]

s = 17.73

s ≈ 17.7

Similarly, by applying cosine rule in the given triangle,

cos(43)° = [tex]\frac{\text{Opposite side}}{Hypotenuse}= \frac{AB}{AC}[/tex]

             = [tex]\frac{r}{26}[/tex]

r = 26[cos(43)°]

r = 19.02

r ≈`19.0

Anyone know how to do this people are answering the question but aren’t choosing two anwsers

Answers

Answer:

Option B and Option D are the two answers

Other Questions
5. Carlotta's Beauty Supply store sells two brands of bar soap. A 6 pack of Brand A costs$6.78 and an 8 pack of Brand B costs $8.40. What brand is the better buy? 1. Which of the following languages is not spoken widely in Spain? - single term algebraic expression is called? A. Monomial earn points!!! B. Binomial C. Trinomial D. None of these A group of puppies have different fur colors. This is an example oforganism diversityecosystem diversitygenetic diversityspecies diversity to transmit heat sound or electricity through a medium Who elects or appoints Representative and Senators?(Marking brainliest for the quickest correct answer!) 1) the president 2) the electoral college 3) The people please help ASAP!! please someone! Will mark brainlyASAPTRy to solve both pls When an Anglo/Saxon poet refersto the sun as "Heaven's brightcandle" or to a deer as a"heather-stepper," he is using apoetic technique known as a(n) How many castes existed in Ancient India? Will mark brainliest :) Given vectors u = -9i + 8j and v = 7i + 5j find 2u -6j in terms of unit vectors i and j(answer choices below vv) Find the m Angle J if m Angle K = 29 and they are complementary angles. The muscle that pumps blood throughout your body is:Cardiac muscleValentine muscleSkeletal muscleSmooth muscle Which of the following would be a good topic sentence for an illustrationparagraph? What was Ben's contribution to his father's Citizenship test? * A) He encouraged his father to become an American citizen.B)He helped his father memorize the Pledge of Allegiance.C)He drove him to the test.D)He planned a celebration after his father passed. Please help me 20 points for whoever can answer this correctlyIf GH = 7x + 18 and JK = 81, find x.38.645514.149 QUICK whoever gives the correct answer gets Brainliest ome athletes now wear special shoes with spikes to get a better grip. What does this indicate? 100 POINTS + BRAINLYIESTRead the list of types of exercise.Decide which component of fitness category each type of exercise belongs in.BikingPush-UpsStretchingEating lean proteinDoing a variety of activitiesDancingJump-ropeSquatsSit-upsSwimmingYogaEating fruitsTouching your toesRiding a bikeBicep curls with dimbbellsAvoiding junk foodRunningEating vegetablesCategories: Cardio Fitness, Muscle strength, Muscle Endurance, Flexibility. Machinery purchased for $73,800 by Blossom Co. in 2016 was originally estimated to have a life of 8 years with a salvage value of $4,920 at the end of that time. Depreciation has been entered for 5 years on this basis. In 2021, it is determined that the total estimated life should be 10 years with a salvage value of $5,535 at the end of that time. Assume straight-line depreciation.Required:Prepare the entry to correct the prior years' depreciation, if necessary.