Question

How do you verify `(1-sin^2Ѳ)(1+cot^2Ѳ)=cot^2Ѳ`?

Answer 1

`f(t) = (1 - sin^2 t)(1 + cot^2 t)`
Transform the first factor:
`(1 - sin^2 t) = cos^2t`
Transform the second factor:
`(1 + cos^2 t/sin^2 t) = (sin^2 t + cos^2 t)/(sin^2 t) = 1/sin^2 t`
Finally,
`f(t) = (cos^2 t)(1/sin^2 t) = cot^2 t` Proved