Question

How do you prove `cot^2 x +csc^2 x = 2csc^2 x - sin^2(2x)-cos^2(2x)`?

Answer 1

See below.

Explanation:

We have:

`cos^2x/sin^2x + 1/sin^2x = 2/sin^2x - (sin^2(2x) + cos^2x)`

`(cos^2x + 1)/sin^2x = 2/sin^2x - 1`

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

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

Hopefully this helps!