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  4. Sum of maximum and minimum value of the function f(x)= sin 2 x+8 cos x-7 is

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Q. Sum of maximum and minimum value of the function $f(x)=\sin ^{2} x+8 \cos x-7$ is

Trigonometric Functions

Solution:

$y=\sin ^{2} x+8 \cos x-7$
$1-\cos ^{2} x+8 \cos x-7$
$=-\left[\cos ^{2} x-8 \cos x+6\right]$
$=-\left[(\cos x-4)^{2}-10\right]$
$=10-(4-\cos x)^{2}$
$\therefore y_{\min .}=10-16=-6$
$y_{\text {max. }}=10-9=1$