Question

How do you prove `cot^2 A csc^2 A - cot^2 A = cot^4 A`?

Answer 1

Replace cot by `cos/sin` in left side.

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

`= ((cos^2 x)(1 - sin^2 x))/(sin^4 x)`= `cos^4 x/sin^4 x = cot^4 x`