Prove that `(cos3x)/(sin2xsin4x)+(cos5x)/(sin4xsin6x)+(cos7x)/(sin6xsin8x)+(cos9x)/(sin8xsin10 x)` = `1/2(cos e cx)[cos e c2x-cos e c10x]`

Explanation

To prove the equation

\[ \frac{\cos 3x}{\sin 2x \sin 4x} + \frac{\cos 5x}{\sin 4x \sin 6x} + \frac{\cos 7x}{\sin 6x \sin 8x} + \frac{\cos 9x}{\sin 8x \sin 10x} = \frac{1}{2} \cos x [\cos 2x - \cos 10x], \]

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

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