Question

Question #a263e

Answer 1

I'm going to assume you mean `cotthetasintheta=(1-sin^2theta)sectheta`, correct me if I'm wrong.

Explanation:

Working the right side, first use the Pythagorean identity `sin^2theta+cos^2theta=1` to know that `1-sin^2theta=cos^2theta`.
`(1-sin^2theta)sectheta=cos^2thetasectheta`.

Then, substitute `1/costheta` for `sectheta` and simplify.
`cos^2thetasectheta=cos^2theta/costheta=costheta`.

Then multiply by `1` in the form of `sintheta/sintheta`.
`costheta=(costhetasintheta)/sintheta`.

And substitute `cottheta` for `costheta/sintheta`.
`(costhetasintheta)/sintheta=cotthetasintheta`

Therefore, `(1-sin^2theta)sectheta=cotthetasintheta`
Q.E.D.