Let X={x in R: cos (sin x)=sin (cos x)} . The | vedclass

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Question

(a)

We have,

$X=\{x \in R: \cos (\sin x)=\sin (\cos x)\}$

$\cos (\sin x)=\sin (\cos x)$

$\quad \sin \left(\frac{\pi}{2} \pm \sin x\right)=

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Vedclass · Answer

(a)

We have,

$X=\{x \in R: \cos (\sin x)=\sin (\cos x)\}$

$\cos (\sin x)=\sin (\cos x)$

$\quad \sin \left(\frac{\pi}{2} \pm \sin xight)=\sin (\cos x)$

$\Rightarrow \quad \cos x=\frac{\pi}{2} \pm \sin x$

$\Rightarrow \cos x=n \pi+(-1)^n\left(\frac{\pi}{2}+\sin xight), n \in I$

$\Rightarrow \cos x \pm \sin x=n \pi+(-1)^n \frac{\pi}{2}, n \in I$

As $L H S \in[-\sqrt{2}, \sqrt{2}]$ and it does not satisfy the RHS.

$	herefore$ No solution exists.

Let $X=\{x \in R: \cos (\sin x)=\sin (\cos x)\} .$ The number of elements in $X$ is

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