Question

prove that cot(theta)+tan(theta)=csc^2(theta)+sec^2(theta)/csc theta sec theta

Answer 1

The expression can be written in terms of sin and cos. As there's no theta symbol on my device I've used ø. Let s=sinø and c=cosø.

First let's prove the identity for one value of ø, and let ø=45 degrees, so c=s=sqrt(2)/2.

That means 1+1=2 (left side). The right side has to be interpreted as (2+2)/(sqrt(2))^2=4/2=2.

Take the right side of the identity:

(1/s^2+1/c^2)/(1/sc)=(1/s^2+1/c^2)*sc=c/s+s/c=left side, because cotø=c/s and tanø=s/c.