Question

((1-sinθ)(1+sinθ))/(〖sin〗^2 θ)=〖cot〗^2 θ

Answer 1

see explanation

Explanation:

Using the trigonometric identities

sin²x + cos²x = 1 ⇒ 1 - sin²x = cos²x

cot x =
`(cosx)/(sinx)`

Consider the left side

`((1-sin0)(1+sin0))/(sin^20)` ← expand numerator using FOIL

=
`(1-sin^20)/(sin^20)`

=
`(cos^20)/(sin^20)`

= cot²Θ = right side