Question

(cscx + 1)(cscx - 1)/ csc² x

Answer 1

cos²x

Explanation:

using the identity

cscx =
`(1)/(sinx)` and 1 - sin²x = cos²x

then

`((cscx+1)(cscx-1))/(csc^2x)` ← expand numerator using FOIL

=
`(csc^2x-1)/((1)/(sin^2x) )`

= (
`(1)/(sin^2x)` - 1 ) × sin²x

= sin²x(
`(1)/(sin^2x)` - 1) ← distribute parenthesis

= 1 - sin²x

= cos²x