Question11. Prove each identity. a) $\frac{\cos 2 x+1}{\sin 2 x}=\cot x$ h) $\csc 2 x+\cot 2 x=\cot x$ b) $\frac{\sin 2 x}{1-\cos 2 x}=\cot x$ i) $\frac{2 \tan x}{1+\tan ^{2} x}=\sin 2 x$ c) $(\sin x+\cos x)^{2}=1+\sin 2 x$ d) $\cos ^{4} \theta-\sin ^{4} \theta=\cos 2 \theta$ j) $\sec 2 t=\frac{\csc t}{\csc t-2 \sin t}$ e) $\cot \theta-\tan \theta=2 \cot 2 \theta$ f) $\cot \theta+\tan \theta=2 \csc 2 \theta$ k) $\csc 2 \theta=\frac{1}{2}(\sec \theta)(\csc \theta)$ g) $\frac{1+\tan x}{1-\tan x}=\tan \left(x+\frac{\pi}{4}\right)$ 1) $\sec t=\frac{\sin 2 t}{\sin t}-\frac{\cos 2 t}{\cos t}$