Question

How do you use the fundamental identities to prove other identities?

Answer 1

Divide the fundamental identity `sin^2x + cos^2x = 1` by `sin^2x` or `cos^2x` to derive the other two:

`sin^2x/sin^2x + cos^2x/sin^2x = 1/sin^2x`

`1 + cot^2x = csc^2x`

`sin^2x/cos^2x + cos^2x/cos^2x = 1/cos^2x`

`tan^2x + 1 = sec^2x`