Question

How do you verify the identity `1/(csctheta+1)+1/(csctheta-1)=2sec^2thetasintheta`?

Answer 1

See below.

Explanation:

`1/(csctheta+1)+1/(csctheta-1)=2sec^2thetasintheta`

`1/(csctheta+1)+1/(csctheta-1)=2csctheta/(csc^2theta-1)=`

`=2(sin^2 theta csc theta) /cos^2theta = 2sin^2theta sec^2theta/sintheta = 2sin theta sec^2theta`