Prove that
`(cos 3 x)/(sin 2 xsin 4x)+(cos 5x)/(sin 4xsin 6x)+(cos 7x)/(sin 6xsin 8x)+(cos 9x)/(sin 8x sin 10x)`
`=(1)/(2) (co sec x)[co sec2x-co sec 10x]`

Explanation

To prove the equation

\[ \frac{\cos 3x}{\sin 2x \sin 4x} + \frac{\cos 5x}{\sin 4x \sin 6x} + \frac{\cos 7x}{\sin 6x \sin 8x} + \frac{\cos 9x}{\sin 8x \sin 10x} = \frac{1}{2} \csc x \left( \csc 2x - \csc 10x \right) \]

we will start with the left-hand side (LHS) and manipulate it step by step.

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