Question

How do you verify the identity `sec^2thetacsc^2theta=sec^2theta+csc^2theta`?

Answer 1

For Proof, see the Explanation below.

Explanation:

`sec^2thetacsc^2theta=1/cos^2theta*1/sin^2theta=1/(cos^2thetasin^2theta)`

`=(cos^2theta+sin^2theta)/(cos^2thetasin^2theta)`

`=cos^2theta/(cos^2thetasin^2theta)+sin^2theta/(cos^2thetasin^2theta)`

`=1/sin^2theta+1/cos^2theta`

`=csc^2theta+sec^2theta`.

Hence, the Proof.