Question

How do you show that `sintheta(cot theta + tantheta) = sec theta`?

Answer 1

Apply the identities `cottheta = costheta/sintheta` and `tantheta = sintheta/costheta`.

`sintheta(costheta/sintheta + sintheta/costheta) = sectheta`

`costheta + sin^2theta/costheta = sectheta`

`(cos^2theta + sin^2theta)/costheta = sectheta`

Apply `cos^2theta + sin^2theta = 1`:

`1/costheta = sectheta`

This is true, by the identity `sectheta = 1/costheta`.

Hopefully this helps!