so i have my end of prelims coming up and doing a revision test. this question came up

$\displaystyle prove (sec^2x - 1)cos^2x = sin^2x $

Now i thought that you would do the question like this:

$\displaystyle LHS = (sec^2x-1)cos^2x = (Tan^2x)cos^2x

= \frac{\sin^2x}{cos^2x} cos^2x

=sin^2x

$

but it gave a different soln. am i wrong?