Question

The maximum value of
$\cos x\left(\frac{\cos x}{1-\sin x}+\frac{1-\sin x}{\cos x}\right)$ is

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is C $2$

$f\left(x\right)=\cos x\left(\frac{{\cos }^{2}x+1+{\sin }^{2}x-2\sin x}{\cos x(1-\sin x)}\right)$$=\cos x\left(\frac{2(1-\sin x)}{\cos x(1-\sin x)}\right)=\cos x\left(\frac{2}{\cos x}\right)=2$