The greatest value of the function $y = {sin}^{2} x - 20 cos x + 1$ is

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Solution

$y = {sin}^{2} x - 20 cos x + 1 y^{'} = 2 sin x cos x + 20 sin x y^{''} = 2 cos 2 x + 20 cos x s o y^{'} = 0 i f sin x = 0 x = 0, π y^{''} < 0 i s a t x = π . y (π) = 20 + 1 = 21$

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