Question

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

• A. -4
• B. -5
• C. 4
• D. 5

Answer 1

Answer: (B)

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