More Trigonometric Proofs?

Question

Hello,

There are some questions that I am not sure how to tackle:

1) cosecθ - sinθ = cotθ cosθ

2) cos^2θ - sin^2θ = 2cos^2θ - 1

3) cosec^2θ + sec^2θ = cosec^2θ sec^2θ

4) (sin^2θ) / (1 - cosθ) = 1 + cosθ

Thank you in advance.

Answer 1

1) Left hand side identity

= Right hand side identity.

2) Left hand side identity

= Right hand side identity.

3) Left hand side identity

= Right hand side identity.

4) Left hand side identity

Multiply numarator and denominator by 1+ cos(θ)

= Right hand side identity.