Could someone double check this problem for me please?

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

- tan^2 x + sec^2 x = 1

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

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

The sin/cos terms cancel each other out and we are left with 1=1

Did I do this right? Thanks for your help.