Question

The value of $2 \cos x-\cos 3 x-\cos 5 x$ is equal to

(A) $16 \cos ^3 x \sin ^2 x$

(B) $16 \sin ^3 x \cos ^2 x$

(C) $4 \cos ^8 x \sin ^2 x$

(D) $4 \sin ^3 x \cos ^2 x$

Answer 1

$2 \cos x-\cos 3 x-\cos 5 x$

$\begin{array}{l}=2 \cos x-2 \cos x \cos 4 x \\=2 \cos x(1-\cos 4 x)=2 \cos x \cdot 2 \sin ^2 2 x \\=4 \cos x(2 \sin x \cos x)^2=16 \sin ^2 x \cos ^3 x\end{array}$

So, The correct option will be (A).