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

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Solution

The correct option is C 21
$f^{1} (x) = 2 s i n x c o s x + 20 s i n x$
$= 2 s i n x (c o s x + 10)$
$f^{1} (x) > 0$ $x ϵ (0, π)$
$f^{1} (x) < 0$ $x ϵ (π, 2 π)$
$f (x)$ is maximum at $x = π$
$f (π) = 0 + 20 + 1$
$= 21$

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