Question

Question #004aa

Answer 1

The two sides are not equivalent.

Explanation:

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

Using FOIL, multiply out the left hand side.

`1+sec(theta)-cos(theta)-cos(theta)sec(theta)`

Convert the `sec`

`1 +1/cos(theta)-cos(theta)-cos(theta) 1/cos(theta)`

`cancel(1 )+ 1/cos(theta) - cos(theta) - cancel(1)`

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

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

`sin^2(theta)/cos(theta)` or `sin(theta)tan(theta)`

This is not equivalent to the right hand side, `sin^2(theta)`. You can also see that they are not equivalent by looking at the graphs of both sides.

![Desmos.com and MS Paint]()