SOLUTION: Prove or disprove without a calculator. (sin theta/csc 2theta)-(cos 2theta/sec theta)= -cos 3theta

Algebra ->  Trigonometry-basics -> SOLUTION: Prove or disprove without a calculator. (sin theta/csc 2theta)-(cos 2theta/sec theta)= -cos 3theta      Log On


   

Question 139752: Prove or disprove without a calculator.
(sin theta/csc 2theta)-(cos 2theta/sec theta)= -cos 3theta
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I'm presuming that you mean %28sin%28x%29%2Fcsc%5E2%28x%29%29-%28cos%5E2%28x%29%2Fsec%28x%29%29=-cos%5E3%28x%29 rather than %28sin%28x%29%2Fcsc%282x%29%29-%28cos%282x%29%2Fsec%28x%29%29=-cos%283x%29, because the second one is a horror I have no intention of spending the rest of the afternoon solving.

sin%28x%29=1%2Fcsc%28x%29 (read is identical to), so 1%2Fcsc%5E2%28x%29=sin%5E2%28x%29 and
cos%28x%29=1%2Fsec%28x%29

So:
, except where sin%28x%29=0