How do I prove $\csc^4 x-\cot^4x=(1+\cos^2x)/\sin^2x$

Question

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-

Answer 1

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

Answer 2

There is an explanation to your problem at http://www.algebra.com/algebra/homework/Trigonometry-basics.faq.question.43447.html.