Integrate : $\int \large\frac{\cos x - \sin x}{\sqrt {\sin 2x}}$$dx$

Question

$(a)\;\log |(\sin x+\cos x ) +\sqrt {\cos 2x}|+c \\(b)\; \log |(\sin x+\cos x ) +\sqrt {\sin 2x}|+c \\(c)\;\sqrt {\sin 2x} \\ (d)\;None$