Question

What is the answer of 1-cot²a=?

Answer 1

It helps to rewrite in terms of sine and cosine.

`1 -cot^2a = 1-cos^2a/sin^2a = (sin^2a -cos^2a)/sin^2a =-(cos^2a -sin^2a)/sin^2a = -cos(2a)/sin^2a`

Hopefully this helps

Answer 2

`- (cos 2a)/sin^2 a`

Explanation:

First answer:
`f(a) = (1 - cot^2 a) = (1 - cot a)(1 + cot a)`
We can go further:
`f(a) = (1 - cos a/(sin a))(1 + cos a/(sin a)) =`
`f(a) = ((sin a- cos a)/(sin a))((sin a + cos a)/(sin a))`
`f(a) = (sin^2 a - cos^2 a)/sin^2 a = - (cos 2a)/(sin^2 a)`