Question

How do you prove `cos^2alphacot^2alpha=cot^2alpha-cos^2alpha`?

Answer 1

`RHS=cot^2alpha-cos^2alpha`

`=cos^2alpha/sin^2alpha-cos^2alpha`

`=cos^2alpha(1/sin^2alpha-1)`

`=cos^2alpha/sin^2alpha(1-sin^2alpha)`

`=cot^2alphacos^2alpha=LHS`

Proved