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$If f (x) = \{\begin{array}{ll} (\cos x)^{\frac{1}{\sin x}} for x \neq 0 \\ k for x = 0 \end{array} then value of k, so that f is differentiable at x = 0 is$

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Correct option is B

Ltx→0 cosx1sinx=kk=eLtx→01sinxlogcosx=eLtx→0 −tanxcosx=e0=1

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If f(x)=(cos⁡x)1sin⁡x for x≠0k for x=0 then value of k, so that f is differentiable at x=0 is

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$If f (x) = \{\begin{array}{ll} (\cos x)^{\frac{1}{\sin x}} for x \neq 0 \\ k for x = 0 \end{array} then value of k, so that f is differentiable at x = 0 is$