The trigonometric relation `tan^2x-sin^2x=tan^2x*sin^2x` has to be verified.

Start from the left hand side

`tan^2x-sin^2x `

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

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

= `((sin^2x)/(cos^2x))*sin^2x`

= `tan^2x*sin^2x`

**This proves that `tan^2x-sin^2x=tan^2x*sin^2x` **