Question

evaluate cos^2((π/4)+x)-sin ^2((π/4)-x)

Answer 1

Here is the ans
Hope it helps you

Answer 2

Given:

$cos^2(\frac{\pi}{4}+x)-sin^2(\frac{\pi}{4}-x)$

To find :

The value of given expression

Solution:

$cos^2(\frac{\pi}{4}+x)-sin^2(\frac{\pi}{4}-x)$

$cos(\frac{\pi}{4}+x+\frac{\pi}{4}-x)cos(\frac{\pi}{4}+x-\frac{\pi}{4}+x)$

Using identity:

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

$cos(\frac{2\pi}{4})cos(2x)$

$cos(\frac{\pi}{2})cos(2x)$

$0\times cos(2x)=0$

Using value

$cos(\frac{\pi}{2})=0$

$cos^2(\frac{\pi}{4}+x)-sin^2(\frac{\pi}{4}-x)=0$