Trigonometric Identities help How do you solve this? I can't figure out what I should do. 
$$\sin ^4\left(A\right)+\cos ^2\left(A\right)=\cos ^4\left(A\right)+\sin ^2\left(A\right)$$
Also, why is this equal zero? Can someone explain how that simplifies to be zero? 
$$\frac{\left(\frac{1}{\cos \left(x\right)}\right)-1}{\left(\frac{1}{\cos \left(x\right)}\right)+1}+\frac{\cos \left(x\right)-1}{\cos \left(x\right)+1}$$ 

Note that $\sin^4 A-\cos^4 A=(\sin^2 A-\cos^2 A)(\sin^2 A+\cos^2 A)=\sin^2 A-\cos^2 A$.
For the other question, we have $\frac{1}{\cos x}-1=\frac{1-\cos x}{\cos x}$ and $\frac{1}{\cos x}+1=\frac{1+\cos x}{\cos x}$. When we divide, the $\cos x$ cancel, and we get $\frac{1-\cos x}{1+\cos x}$.
