Question

How do you prove `csc^2xtan^2x-1=tan^2x`?

Answer 1

Prove trig identity

Explanation:

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

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

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

=`sin^2x/cos^2 x = tan^2 x`