Mathematics High School

please someone help me to prove this.

Answers

Answer 1

Answer :

We know that,

[tex]\dag\bf\:sin^2A=\dfrac{1-cos2A}{2}[/tex]

[tex]\dag\bf\:sin2A=2sinA\:cosA[/tex]

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Now, Let's solve !

[tex]\leadsto\:\bf\dfrac{sin^2A-sin^2B}{sinA\:cosA-sinB\:cosB}[/tex]

[tex]\leadsto\:\sf\dfrac{\frac{1-cos2A}{2}-\frac{1-cos2B}{2}}{\frac{2sinA\:cosA}{2}-\frac{2sinB\:cosB}{2}}[/tex]

[tex]\leadsto\:\sf\dfrac{1-cos2A-1+cos2B}{sin2A-sin2B}[/tex]

[tex]\leadsto\:\sf\dfrac{2sin\frac{2A+2B}{2}\:sin\frac{2A-2B}{2}}{2sin\frac{2A-2B}{2}\:cos\frac{2A+2B}{2}}[/tex]

[tex]\leadsto\:\sf\dfrac{sin(A+B)}{cos(A+B)}[/tex]

[tex]\leadsto\:\bf{tan(A+B)}[/tex]

Answer 2

Answer: see proof below

Step-by-step explanation:

Use the Power Reducing Identity: sin² Ф = (1 - cos 2Ф)/2

Use the Double Angle Identity: sin 2Ф = 2 sin Ф · cos Ф

Use the following Sum to Product Identities:

[tex]\sin x - \sin y = 2\cos \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x - \cos y = -2\sin \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)[/tex]

Proof LHS → RHS

[tex]\text{LHS:}\qquad \qquad \qquad \dfrac{\sin^2A-\sin^2B}{\sin A\cos A-\sin B \cos B}[/tex]

[tex]\text{Power Reducing:}\qquad \dfrac{\bigg(\dfrac{1-\cos 2A}{2}\bigg)-\bigg(\dfrac{1-\cos 2B}{2}\bigg)}{\sin A \cos A-\sin B\cos B}[/tex]

[tex]\text{Half-Angle:}\qquad \qquad \dfrac{\bigg(\dfrac{1-\cos 2A}{2}\bigg)-\bigg(\dfrac{1-\cos 2B}{2}\bigg)}{\dfrac{1}{2}\bigg(\sin 2A-\sin 2B\bigg)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{1-\cos 2A-1+\cos 2B}{\sin 2A-\sin 2B}\\\\\\.\qquad \qquad \qquad =\dfrac{-\cos 2A+\cos 2B}{\sin 2A - \sin 2B}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 2B-\cos 2A}{\sin 2A-\sin 2B}[/tex]

[tex]\text{Sum to Product:}\qquad \qquad \dfrac{-2\sin \bigg(\dfrac{2B+2A}{2}\bigg)\sin \bigg(\dfrac{2B-2A}{2}\bigg)}{2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\sin \bigg(\dfrac{2A-2B}{2}\bigg)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{-2\sin (A + B)\cdot \sin (-[A - B])}{2\cos (A + B) \cdot \sin (A - B)}[/tex]

[tex]\text{Co-function:}\qquad \qquad \dfrac{2\sin (A + B)\cdot \sin (A - B)}{2\cos (A + B) \cdot \sin (A - B)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \quad \dfrac{\cos (A+B)}{\sin (A+B)}\\\\\\.\qquad \qquad \qquad \quad =\tan (A+B)[/tex]

LHS = RHS: tan (A + B) = tan (A + B) [tex]\checkmark[/tex]

Related Questions

А
B
1. Village A, B and C lie on the edge of the Namib Desert.
Village A is 30 km due North of Village C. Village C is 65 km
due East of A.
Calculate the shortest distance between village C and B,
giving your answer to the nearest 0.1km

Answers

There answer would be A

You spend $300 to start and costs $20 for each dog house
# of dog houses
1
2.
3
4
5
6
7
Total cost to build

Answers

Answer:

Step-by-step explanation:

because because 300 divided by 20 equals 15 hope this helps

Owen is fishing from a dock he starts with the bait 2 feet below the surface he reels out the boat 19 feet then reels it back in 7 feet what is the final position of the bait relative to the surface of the water

Answers

Answer:

The bait is 14 feet below the water surface

Step-by-step explanation:

Here, we want to know the final position of the bait relative to the surface of the water.

Firstly, he starts with the bait at 2 feet below the water surface. The reels out the bait a further 19 feet, the new position of the bait relative to the water surface will be 2 + 19 = 21 feet

Now, he reels the bait back by 7 feet.

Thus, the new depth of the bait relative to the water surface will be 21-7 = 14 feet

Lucy is going to walk in a fundraising event to raise money for her school band. Her mother has agreed to donate $7.50 to the school for each mile that Lucy walks, plus an additional $25. If Lucy wants to make at least $85.00 from her mother’s donation, how far will she have to walk? Show your work.

Answers

Answer:

8 miles

Step-by-step explanation:

let x= miles she walks

7.50x+25=85

subtract 25 from both

7.50x=60

divide both by 7.50

x=8

The ratio of yellow to blue skittles in a bag 5:9 if there are 12 more blue skittles in the bag than yellow skittles how many yellow skittles are in the bag

Answers

Answer: 15

Step-by-step explanation: 5/9=15/27. 27-15=12

The number of yellow skittles in the bag are 15 skittles while the number of blue skittles in the bag are 27 skittles.

What is Ratio?

A ratio is an ordered pair of numbers x and y which can be written as x / y where y does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

For given information,

The ratio of yellow to blue skittles in the bag is 5:9

The number of blue skittles in the bag = 12 + The number of yellow skittles in the bag= 12+Y

Fraction of the total skittles that are yellow = 5/(5 + 9) = 5/14

Fraction of the total skittles that are blue = 9/(5+9)= 9/14

The total number of skittles = Yellow + Blue

in this Y as yellow; Y+12 as blue.

Y + Y + 12 = 2·Y + 12

The fraction of the total skittles that are blue = 9/14

we have 9/14 × (2·Y + 12) = Y + 12

-> 9 × (2·Y + 12) = 14 × (Y + 12)

-> 18·Y + 108 = 14·Y + 168

-> 18·Y - 14·Y = 168 - 108 = 60

-> 4·Y = 60

-> Y = 60/4 = 15

∴ The number of yellow skittles in the bag = 15

The number of blue skittles is given as = Y + 12 = 15 + 12 = 27.

Thus, the number of yellow skittles in the bag are 15 skittles while the number of blue skittles in the bag are 27 skittles.

Learn more about Ratio, here:

https://brainly.com/question/13419413

#SPJ5

Danny is trying to determine the product between a rational and irrational number

Answers

Answer:

2√3=2√3, which is irrational

Which represents a function

Answers

Answer:

the one on the right

Step-by-step explanation:

one input cannot have more than one output

Simplify: -3(y+2)^2-5+6y

Answers

Answer:3y^2+18y+7

:) happy to help

How much should Jenna save up to prepare for car repairs and maintenance? (A lump sum emergency fund just for car repair/maintenance that may come up in the future)

Answers

Answer:

$500 per year.

Step-by-step explanation:

Car repairs and maintenance expense is based on the usage of car as well as its present condition. If the car is bought from showroom and is new then it will incur only small amount of expense as its maintenance but if the car is used by various owners then it is likely that maintenance expense can be huge. The average car repair expense is $500 to $800 per year depending on car condition. Since Jenna car is new she should keep the repair estimate to be minimum that is nearly $500 per year or $42 per month.

I NEED SERIOUS HELP NOW PLZ
The expression (y – 9)2 is equivalent to which expression. Simplify and write in standard form. Show your work.

Answers

Answer:

Step-by-step explanation:

Hello,

[tex](y-9)^2=(y-9)(y-9)=y^2-2*9*y+9^2=y^2-18y+81[/tex]

thanks

Answer:

yes

Step-by-step explanation:

Henry needs 2 pints of red paint and 3 pints of yellow paint to get a specific shade orange. If he uses 9 pints of yellow paint and wants the same orange color, how many pints of paint will he need altogether. Explain how you know

Answers

Answer:

15 pints of paint 6 red 9 yellow

Step-by-step explanation:

3x3=9 so 9 yellow pints

and 2x3=6 so 6 red pints

6+9=15 so 15 pints of paint in total

Twelve more than a number is the product of -3 and 6. Translate using n

Answers

Answer: n + 12 = -18 or n + 12= -3(6)

Step-by-step explanation:

12 more than a number means 12 is added to the number so the expression will be n + 12 and the product of -3 and 6 is the same as -3 times 6 which is -18 . n + 12 has to equal -18 .

n + 12 = -18 now subtract 12 from both sides

-12 -12

n= -30

So the number is -30

is 4 √ 7 2 written in simplest radical form

yes or no

Answers

Answer:

No.

Step-by-step explanation:

Notice that 72 can be written as 8 * 9.

4√72 = 4(√8)(√9) = 4(√8)(3) = 12√8.

Hence the answer is No.

Answer:

no 8[tex]\sqrt{7}[/tex] would be simplified

Step-by-step explanation:

A 12.5 oz box of cereal has a price of $2.07. What is the unit ratio of price to weight rounded to the nearest cent?

Answers

Answer:

16 cents

Step-by-step explanation:

The answer is 16 cents because 207 cents divided by 12.5 oz equals 16 cents.

Jesse loves to go hiking on rustic trails through trees and along rivers. One day in 20 minutes of hiking she hiked 1 mile. If Jesse hike at a constant rate what would the rate be

Answers

Answer:

0.05 mile per minutes

Step-by-step explanation:

Jesse's rate of hiking (miles per minute) = Total miles covered / Time covered

Miles covered = 1 mile

Time covered = 20 minutes

Jesse's rate of hiking (miles per minute) = Total miles covered / Time covered(minutes)

= 1 mile / 20 minutes

= 0.05 mile per minutes

20 minutes

= 20 × 60 seconds

= 1200 seconds

Jesse's rate of hiking (miles per seconds) = Total miles covered / Total time taken (seconds)

= 1 mile / 1200 seconds

= 0.0008333333333 miles per seconds

Approximately 0.000833 miles per seconds

Si la época prehistórica sucedió desde hace 2.5 millones de años a.C., hasta hace 2.500 años a.C.; el período Paleolítico (2.5 millones de años a.C. Hasta 10.000 a.C.; el Mesolítico 10.000 a.C. Hasta 5.000 a.C. Y, el Neolítico sucedió desde el 5.000 a.C. Hasta el 2.500 a.C. ¿A qué fracción de la época prehistórica corresponde el período paleolítico? *

Answers

Answer:

El período paleolítico corresponde a [tex]\frac{332}{333}[/tex] de la época prehistórica.

Step-by-step explanation:

En primer lugar, se determina la extensión de tiempo, medida en años, tanto de la época prehistórica como el período paleolítico: (Nótese que el signo negativo significa a.C.)

Época Prehistórica

[tex]\Delta T = -2500-(-2500000)[/tex]

[tex]\Delta T = 2497500\,years[/tex]

Período Paleolítico

[tex]\Delta t = -10000 - (-2500000)[/tex]

[tex]\Delta t = 2490000\,years[/tex]

La fracción de la época prehistórica que corresponde al período paleolítico es:

[tex]r = \frac{\Delta t}{\Delta T}[/tex]

[tex]r = \frac{2490000\,years}{2497500\,years}[/tex]

[tex]r = \frac{332}{333}[/tex]

El período paleolítico corresponde a [tex]\frac{332}{333}[/tex] de la época prehistórica.

The ratio of the number of baskets made by to Tony to the number of baskets made by Colin is 2 to 3. Tony made 10 baskets.How many baskets did Colin make?

Answers

Answer:

I believe the answer would be 15

Step-by-step explanation:

This is because the ratio is 2 to 3 and you would divide it in half so you get one part then times it by three to get the second part of the ratio.

So it would be 10/2=5 then 5 times 3 to get 15. Therefore, 10 to 15

Answer:

15 baskets

Step-by-step explanation:

Step 1 : write a statement

Tony : Colin

2 : 3

10 : ?

Step 2: Cross multiply

i.e. 10×3=30

30÷2=15

A rectangle has height to width ratio 3:45. give two examples of dimensions for rectangles that could be scaled version of this rectangle

Answers

Answer:

fr7diyktgjhv fdxgkhgfdxghnjkngfcc

Step-by-step explanation:

rd6klfutgkhjkhfdeswdfgkjhuyt6rdefgthjkiluhgf

Answer:

Step-by-step explanation:

1) f(x) = 3x - 4
g(x) – x2 + 3x
Find f(g(x))

Answers

Answer:

x=4/3

Step-by-step explanation:

Figures in square brackets are estimated standard errors of the coefficient estimates. What is the value of the test statistic for the hypothesis that the coefficient of is zero against the alternative that is less than zero?

Answers

Umm I’m not sure. Sorry for the inconvenience.

Find the straight pay:$9.25 per hour x 35 hours.

Answers

Answer:

323.75 hours is the answer

Using inductive reasoning, what number is the most reasonable conjecture for the next number in the pattern 27,23,19,15,

Answers

Answer:

Step-by-step explanation:

The pattern here is to subtract by 4, so 15-4=11

I need to know about the gradient

Answers

Answer:

Step-by-step explanation:

How do you divide 506 in the ratio 2:4:5 ?

Answers

Answer:

Step-by-step explanation:

If the ratio is 2:4:5 there are 2+4+5=11 equal parts...

506/11=46

So each part is equal to 46 so 506 in a ratio of 2:4:5 is:

92:184:230

What is the value of 6 x 90.6 ?

Answers

Answer:

543.6

Step-by-step explanation:

=> 6 x 90.6

=> 543.6

Please help, Solve Systems of Linear Equations

Answers

Answer:

x = 1 , y = 1 , z = -3

Step-by-step explanation using elimination:

Solve the following system: