If you meant (sinx/sinx+1)-(sinx/sinx-1)=-2tan^2x it would be wrong it should have said (sinx/sinx+1)-(sinx/sinx-1) = 2tanx(secx)
to prove that add the two terms on the Left Side, by using a common denominator of (sinx+1)(sinx-1), then simplifiying the left side. It reduces very nicely to the Right Side.