Question

How do you verify the identity `cot^2thetacsc^2theta-cot^2theta=cot^4theta`?

Answer 1

See the Explanation.

Explanation:

Since, `csc^2theta=cot^2theta+1`, we have,

The L.H.S.`=cot^2theta(cot^2theta+1)-cot^2theta`

`=cot^4theta+cot^2theta-cot^2theta`

`=cot^4theta`

`="The R.H.S"`.