Question

Question #84c50

Answer 1

See below

Explanation:

`1+(color(red)(sin^2theta))/(cos^2theta)`

Use the following identity to solve for `sin^2theta`

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

`sin^2theta=color(red)(1-cos^2theta)`

Substitute this instead of `sin^2theta`

`1+(sin^2theta)/(cos^2theta)=1+(color(red)(1-cos^2theta))/cos^2theta`

Add `1` and `(1-cos^2theta)/cos^2theta` together by unifying the denominators (`1` is

the same as `cos^2theta/cos^2theta`), so

`color(red)1+(1-cos^2theta)/cos^2theta=color(red)(cos^2theta/cos^2theta)+(1-cos^2theta)/cos^2theta`

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

`=1/cos^2theta`

`=sec^2theta`