A) \[-\frac{1}{4}\]
B) \[-\frac{1}{2}\]
C) \[-\frac{3}{4}\]
D) \[-1\]
Correct Answer: C
Solution :
Given that: \[\sin (\pi \cos x)=\cos (\pi \sin x)\] So, \[\cos \left( \frac{\pi }{2}-\pi \cos x \right)=\cos (\pi \sin x)\] \[\Rightarrow \,\,\frac{\pi }{2}-\pi \cos x=\pi \sin x\] \[\Rightarrow \,\,\sin x+\cos x=\frac{1}{2}\] Squaring both sides, we get \[{{\sin }^{2}}x+{{\cos }^{2}}x+2\sin x\cos x=\frac{1}{4}\] \[\Rightarrow \,\,\sin 2x=\frac{1}{4}-1=-\frac{3}{4}\]You need to login to perform this action.
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