Prove the trigonometric identities?

Question

Hello,

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

1) secθ - cosθ = sinθ tanθ

2) sin^2θ + 2cos^2θ = 2 - sin^2θ

3) tanθ + cotθ = 1 / (sinθ cosθ)

Thank you.

Answer 1

Recall the pythageron identity

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