Question

The value of $\cos y\cos\left( \frac{\pi}{2} - x \right) - \cos\left( \frac{\pi}{2} - y \right)\cos x$

$+ \sin y\cos\left( \frac{\pi}{2} - x \right) + \cos x\sin\left( \frac{\pi}{2} - y \right)$ is zero, if

• A. $x = 0$
• B. $y = 0$
• C. $x = y$
• D. $x = n\pi - \frac{\pi}{4} + y,(n \in I)$

Answer 1

Answer: (D)

$x = n\pi - \frac{\pi}{4} + y,(n \in I)$

Answer 2

The expression is equal to

$\sin(x - y) + \cos(x - y) = \sqrt{2}\left\{ \sin\left( \frac{\pi}{4} + x - y \right) \right\}$,

which is zero, if $\sin\left( \frac{\pi}{4} + x - y \right) = 0$

i.e., $\frac{\pi}{4} + x - y = n\pi(n \in I) \Rightarrow x = n\pi - \frac{\pi}{4} + y$.