Question

Evaluate sin²(15°+A) - sin² (15°-A)

Answer 1

sin(15+A+15-A) sin( 15+A-15+A)
sin30 sin2A
1/2 sin2A
1/2 2sinA cosA
sinA cosA

Answer 2

Answer:

$\sin^2(15^\circ+A)-\sin^2(15^\circ-A) = \frac{1}{2}\sin(2A)$

Step-by-step explanation:

Given : Expression $\sin^2(15^\circ+A)-\sin^2(15^\circ-A)$

To Evaluate : Given expression?

Solution :

We know that  formula,

$\sin^2A-\sin^2B = \sin(A+B) \sin(A-B)$

Substitute the value in the formula,

$\sin^2(15^\circ+A)-\sin^2(15^\circ-A) = \sin(15+A+15-A) \sin(15+A-15+A)$

$\sin^2(15^\circ+A)-\sin^2(15^\circ-A) = \sin(30) \sin(2A)$

$\sin^2(15^\circ+A)-\sin^2(15^\circ-A) = \frac{1}{2}\sin(2A)$

Therefore, $\sin^2(15^\circ+A)-\sin^2(15^\circ-A) = \frac{1}{2}\sin(2A)$