Question

How do you simplify `((1-costheta)(1 + costheta))/((1-sintheta)(1+sintheta))`?

Answer 1

`tan^2theta`

Explanation:

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

We know that `(a+b)(a-b)=a^2-b^2`, so we can convert the expresssion in:

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

Then we know that `cos^2 theta+sin^2 theta=1`:

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