Question

How do you simplify the expression `secthetacos^2theta`?

Answer 1

`secthetacos^2theta=1/costhetacos^2theta=costheta, theta !=pi/2+npi`

Explanation:

Remember that:

`sectheta=1/costheta`

So we can say:

`secthetacos^2theta=1/costhetacos^2theta=costheta`

The constraints of the original still apply to the simplified expression!

So where `secthetacos^2theta` is undefined, so is our simplified version, `costheta`. As is pointed out in the comments below, `sectheta` is undefined where `costheta=0`. Within the range of `[0,2pi)`. That occurs at `pi/2 and (3pi)/2`, and is expressed generally as `pi/2+npi`