A) 0
B) 2
C) 4
D) Not finite
Correct Answer: A
Solution :
| We have, \[\cos (\sin x)=\sin (\cos x)\] |
| \[\Rightarrow \]\[\sin \left( \frac{\pi }{2}\pm \sin x \right)=\sin (\cos x)\] |
| \[\Rightarrow \]\[\cos x=n\pi +{{(-1)}^{n}}\left( \frac{\pi }{2}+\sin x \right),n\in I\] |
| \[\Rightarrow \]\[\cos x\pm \sin x=nx+{{(-1)}^{n}}\frac{\pi }{2},n\in I\] |
| As LHS \[\in [-\,\sqrt{2},\sqrt{2}],\]and it does not satisfies RHS. |
| Hence, no solutions exists. |
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