Proving the identity $(\tan^2(x)+1)(\cos^2(-x)-1)=-\tan^2(x)$ Proving the trigonometric identity $(\tan{^2x}+1)(\cos{^2(-x)}-1)=-\tan{^2x}$ has been quite the challenge. I have so far attempted using simply the basic trigonometric identities based on the Pythagorean Theorem. I am unsure if these basic identities are unsuitable for the situation or if I am not looking at the right angle to tackle this problem.

Hint:
Multiply the two members by $\cos^2x$ (certainly nonzero):
$$(\sin^2x+\cos^2x)(\cos^2x-1)=-\sin^2x.$$
