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

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:

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

Answers

Answer:3y^2+18y+7

:) happy to help

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

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

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.

Solve for d. dt=v What is d equal to? A. d=vt B. d=t/v C. d=v-t D. d=v/t

Answers

Answer: I think the answer is "d = vt"

Step-by-step explanation:

Multiply both sides of the equation by;

t * d = v * (t)

Multiply, v by t

Answer; d = vt

Hope this helps :)

The value of d, is equivalent to d = v/t.

What is a function?

An expression in mathematics defines a relationship between one variable (the independent variable, x) and another variable (the dependent variable, y). For example -

f(x) = 4x + 6

Given is the following equation -

dt = v

We have -

dt = v

d = v/t

Therefore, the value of d, is equivalent to d = v/t.

To solve more questions on functions, visit the link below -

brainly.com/question/26182329

#SPJ5

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: