How do I prove $\csc^4 x-\cot^4x=(1+\cos^2x)/\sin^2x$ How do I prove $\csc^4 x-\cot^4x=\dfrac{(1+\cos^2x)}{\sin^2x}$
Do you start from RHS or LHS? I get stuck after first few steps-

The LHS:
$$\frac{1}{\sin^4 x}-\frac{\cos^4 x}{\sin^4 x}=\frac{1-\cos^4 x}{\sin^4 x}=\frac{(1-\cos^2 x)(1+\cos^2 x)}{\sin^4 x}=\frac{1+\cos^2 x}{\sin^2 x}$$
