• # question_answer If p > 2 then the. maximum value of the function $f\,(x)=\cos 2x+2p\sin x$is: A) $2p-3$ B) $-\,1$ C) $-\,3-2p$ D) $-1+2p$

 $f'\,(x)=-\,2\sin 2x+2p\,\cos x$ $f'\,(x)=-\,2\cos x\,(2\sin x-p)$ Since $p>2$$\Rightarrow$$2\sin x-p<0$ Hence $f'\,(x)$will have same sigh as $\cos \,\,x$ Hence maximum value is at $x=\pi /2$ which is equal to $-1+2p$