The value of cos y cos left( frac{pi}{2} - x | vedclass

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(D) Given expression: $E = \cos y \cos \left( \frac{\pi}{2} - x \right) - \cos \left( \frac{\pi}{2} - y \right) \cos x + \sin y \cos \left( \frac{\pi}

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

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(D) Given expression: $E = \cos y \cos \left( \frac{\pi}{2} - x ight) - \cos \left( \frac{\pi}{2} - y ight) \cos x + \sin y \cos \left( \frac{\pi}{2} - x ight) + \cos x \sin \left( \frac{\pi}{2} - y ight)$.Using the identities $\cos \left( \frac{\pi}{2} - 	heta ight) = \sin 	heta$ and $\sin \left( \frac{\pi}{2} - 	heta ight) = \cos 	heta$,we get:$E = \cos y \sin x - \sin y \cos x + \sin y \sin x + \cos x \cos x$.Wait,let us re-evaluate the expression: $E = \sin x \cos y - \cos x \sin y + \sin y \sin x + \cos x \cos x$.$E = \sin(x - y) + \cos(x - y)$.To make $E = 0$,we have $\sin(x - y) + \cos(x - y) = 0$.$\Rightarrow \sin(x - y) = -\cos(x - y)$.$\Rightarrow 	an(x - y) = -1$.$\Rightarrow x - y = n\pi - \frac{\pi}{4}$.$\Rightarrow x = n\pi - \frac{\pi}{4} + y$,where $n \in I$.

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

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