Let $f(x)=\cos x(\sin x+\sqrt{\sin^2 x+\sin^2\theta})$ where $\theta$ is a given constant then maximum value of $f(x)$ is

Question

$\begin{array}{1 1}(a)\;\sqrt{1+\cos^2\theta}&(b)\;\sqrt{1+\sin^2\theta}\\(c)\;\mid \cos\theta\mid&(d)\;\mid \sin\theta\mid\end{array}$