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The smallest positive value of ‘p’ for which the equation $\cos (P \sin x) = \sin (P \cos x)$ has solution is $0 \leq x \leq 2 π$ is

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$\frac{π}{2 \sqrt{2}}$

$\frac{π}{\sqrt{2}}$

$\frac{3 π}{2 \sqrt{2}}$

$\frac{π}{2}$

answer is C.

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Detailed Solution

$\cos (P \sin x) = \sin (P \cos x)$

$\cos (P \sin x) = \cos (\frac{π}{2} - P \cos x)$

$P \sin x + P \cos x = 2 n π + \frac{π}{2}$

$P \sin x - P \cos x = 2 n π - \frac{π}{2}$

$P (\sin x - \cos x) = 2 n π \pm \frac{π}{2}$

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