Question

How do you prove `tan^2xsin^2x=tan^2x + cos^2x-1`?

Answer 1

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

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

`= tan^2x - 1 + cos^2 x`