Question

How do you verify the identity `csc^2theta/cottheta=cscthetasectheta`?

Answer 1

`csc^2theta/cottheta=(1/sin^2theta)/(costheta/sintheta)`

`=(1/sin^2 theta)(sin theta/cos theta)`

`=(1/sin theta)(1/cos theta)`

`=csc thetasec theta.`