Prove that : `(2 cos 2^n theta + 1)/(2 cos theta +1) = (2 cos theta -1) (2 cos 2theta -1) (2 cos 2^2 theta -1) … (2 cos 2^(n-1) theta -1)`

Explanation

To prove the equation

\[ \frac{2 \cos(2^n \theta) + 1}{2 \cos(\theta) + 1} = (2 \cos(\theta) - 1)(2 \cos(2\theta) - 1)(2 \cos(2^2 \theta) - 1) \cdots (2 \cos(2^{n-1} \theta) - 1), \]

we will start by analyzing the right-hand side (RHS) and simplifying it step by step.

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