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# Express the following as the sum difference of cosines and sines $2\sin 3\theta.\cos\theta$

$\begin{array}{1 1}(A)\;\sin 4\theta+\sin 2\theta\\(B)\;\sin 3\theta+\sin 3\theta\\(C)\;\sin \theta+\cos 2\theta\\(D)\;\text{None of these}\end{array}$

• $2\sin A\cos B=\sin (A+B)+\sin (A-B)$
$2\sin 3\theta\cos \theta=\sin (3\theta+\theta)+\sin (3\theta-\theta)$
$\Rightarrow \sin 4\theta+\sin 2\theta$