Trigonometric Identities Question 282
Question: The value of $ \cos y\cos ( \frac{\pi }{2}-x )-\cos ( \frac{\pi }{2}-y )\cos x $ $ +\sin y\cos ( \frac{\pi }{2}-x )+\cos x\sin ( \frac{\pi }{2}-y ) $ is zero, if
Options:
A) $ x=0 $
B) $ y=0 $
C) $ x=y $
D) $ x=n\pi -\frac{\pi }{4}+y,(n\in I) $
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Answer:
Correct Answer: D
Solution:
The expression is equal to $ \sin (x-y)+\cos (x-y)=\sqrt{2}{ \sin ( \frac{\pi }{4}+x-y ) } $ , which is zero, if $ \sin ( \frac{\pi }{4}+x-y )=0 $ i.e., $ \frac{\pi }{4}+x-y=n\pi (n\in I)\Rightarrow x=n\pi -\frac{\pi }{4}+y $ .
BETA
