Question

How do you simplify the expression `sec^2theta/(sec^2theta-1)`?

Answer 1

`sec^2theta/(sec^2theta-1)=csc^2theta`

Explanation:

`sec^2theta/(sec^2theta-1)`

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

= `(sec^2thetaxxcos^2theta)/(sec^2thetaxxcos^2theta-cos^2theta)`

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

= `1/sin^2theta`

= `csc^2theta`