Question

Question #f837c

Answer 1

I tried this:

Explanation:

We can use the fact that:
`sectheta=1/costheta`
and
`tantheta=(sintheta)/(costheta)`

and write:

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

multiply on the left to get:

`1-cos^2theta=sin^2theta` that it is true!

Remebering that:

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

Answer 2

`(1 - cos theta)(1 + cos theta) sec^2 theta = (1 - cos^2 theta)* 1/cos^2 theta`

note : `sec^2 theta = 1/cos^2 theta` and `1 -cos^2 theta = sin^2 theta`

`(1 - cos^2 theta)* 1/cos^2 theta= sin^2 theta/ cos^2 theta = tan^2 theta` --> proved