Prove that: `(2cos2^ntheta+1)/(2costheta+1)=(2costheta-1)(2cos2theta-1)(2cos2^2theta-1) ...(2cos2^(n-1)theta-1)`

Explanation

To prove the identity

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

we will start from the right-hand side (RHS) and manipulate it to show that it equals the left-hand side (LHS).

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