Question

How do you use the fundamental identities to simplify `tan^2theta/sec^2theta`?

Answer 1

`tan^2theta/sec^2theta=sin^2theta`

Explanation:

We can write:

`tan^2theta/sec^2theta`

as

`(sin^2theta/cos^2theta)/(1/cos^2theta)`

`(sin^2theta/cos^2theta)(cos^2theta/1)`

`(sin^2theta/cancel(cos^2theta))(cancel(cos^2theta)/1)=sin^2theta`