A) 0
B) 1
C) \[-1\]
D) \[\frac{1}{2}\]
Correct Answer: B
Solution :
\[y={{\cos }^{-1}}\left[ \frac{3}{5}\cos x-\frac{4}{5}\sin x \right]\] Putting \[\frac{3}{5}=r\cos \theta ,\,\,\frac{4}{5}=r\sin \theta \Rightarrow r=1\] Þ \[y={{\cos }^{-1}}[\cos \theta \cos x-\sin \theta \sin x]=\theta +x\]\[\Rightarrow \frac{dy}{dx}=1\].
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