Prove the followng identities:

1. tan x.cos x. cosec x = 1

2. (1 + tan2x)(1 − sin2x) = 1

3. 3 − 4 sin2x = 4cos2x − 1

4. sec2x + cosec2x = sec2x cosec2x

5. 

6. cosec x − cos x cot x = sin x

7. 

8. 

9. cos 4x = 1 − 8sin2x cos2x

10.