Find the maximum value of cos (cos(cos x))

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Solution

$The given function is \cos (\cos (\cos x)) We know that for all real vlues of θ, - 1 \leq cosθ \leq 1 . Thus, the maximum possible value of \cos θ is 1 . The function \cos θ decreases from 1 to - 1 as the value of θ increases from 2 nπ to (2 n + 1) π . Now, the function \cos (\cos (\cos x)) wiil be maximum, when \cos (\cos x) will be minimum . The function \cos (\cos x) will be minimum when \cos x has maximum value . The maximum value of \cos x occurs at x = 2 nπ, i . e . the maximum possible value of \cos x is 1 . Hence, the maximum value of \cos (\cos (cosx)) occurs at x = 2 nπ and the maximum value is \cos (\cos (1)) .$

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