The value of `cosycos(pi/2-x)-cos(pi/2-y)cosx+sinycos(pi/2-x)+cosxsin(pi/2-y)` is zero if (A) `x=0` (B) `y=0` (C) `x=y` (D) `npi+y-pi/4(n in Z)`

Explanation

To solve the given expression \( \cos y \cos\left(\frac{\pi}{2} - x\right) - \cos\left(\frac{\pi}{2} - y\right) \cos x + \sin y \cos\left(\frac{\pi}{2} - x\right) + \cos x \sin\left(\frac{\pi}{2} - y\right) = 0 \), we will simplify it step by step.

### Step 1: Use Trigonometric Identities
We know that:
\[ \cos\left(\frac{\pi}{2} - \theta\right) = \sin \theta \]
Using this identity, we can rewrite the expression:
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