The value of $\cos^{2}\left( \frac{\pi}{4} + heta ight) - \sin^{2}\left( \frac{\pi}{2} - heta ight)$ is

Question

The value of $\cos^{2}\left( \frac{\pi}{4} + 	heta ight) - \sin^{2}\left( \frac{\pi}{2} - 	heta ight)$ is

Dr. Abubacker · Accepted Answer

(a)
$\cos^{2}\left( \frac{\pi}{4} + 	heta ight) - \sin^{2}\left( \frac{\pi}{4} - 	heta ight)$
$= \cos\left( \frac{\pi}{4} + 	heta + \frac{\pi}{4} - 	heta ight)\cos\left( \frac{\pi}{4} + 	heta - \frac{\pi}{4} + 	heta ight)$
$= \cos{\left( \frac{\pi}{2} ight)\cos{(2	heta) = 0}}$

Q. The value of $\cos^{2}\left( \frac{\pi}{4} + \theta \right) - \sin^{2}\left( \frac{\pi}{2} - \theta \right)$ is

Explanation

Reviewed by Dr. Abubacker

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