Question

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

• A. $-4$
• B. $-5$
• C. $4$
• D. $-14$

Answer 1

The correct option is A $-4$

we have given that

$f\left(x\right)=2\sin x\cos x-8\sin x----\left(1\right)$

For maximum and minimum value

$f^{\prime }\left(x\right)=0$

$\Rightarrow 2\sin x\cos x-8\sin x=0$

$\Rightarrow 2\sin x\left(\cos x-4\right)=0$

$cosx=4$

$sinx=0$

$value=-4$

Hence, the option $\left(A\right)$ is correct.