Prove the identities

1. $$\frac{2}{\sec x+\text{cosec}x}=\tan 2x(\cos x-\sin x)$$
2. $$\cot 2x{\sec }^{2}x\tan x=\frac{1-{\tan }^{4}x}{2}$$
3. $$\tan \theta +\cot \theta =2\text{cosec}2\theta$$