The maximum value of sin (cos (tan x)) is | vedclass

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(B) Let $f(x) = \sin (\cos (	an x))$.We know that the range of the tangent function $	an x$ is $(-\infty, \infty)$.Therefore,the range of $\cos (	a

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$\sin 1$

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(B) Let $f(x) = \sin (\cos (	an x))$.We know that the range of the tangent function $	an x$ is $(-\infty, \infty)$.Therefore,the range of $\cos (	an x)$ is $[-1, 1]$.Let $u = \cos (	an x)$,so $u \in [-1, 1]$.We want to find the maximum value of $g(u) = \sin u$ for $u \in [-1, 1]$.Since the sine function is strictly increasing on the interval $[-1, 1]$,the maximum value occurs at the largest value of $u$,which is $u = 1$.Thus,the maximum value is $\sin(1)$.

The maximum value of $\sin (\cos (\tan x))$ is

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