Answer Q 27 (or part)

LHS = \sqrt{2 + \sqrt{2 + \sqrt{2 + 2 \cos 8 θ}}} = \sqrt{2 + \sqrt{2 + \sqrt{2 (1 + \cos 8 θ)}}} = \sqrt{2 + \sqrt{2 + \sqrt{2 . 2 \cos^{2} 4 θ}}} = \sqrt{2 + \sqrt{2 + 2 \cos 4 θ}} = \sqrt{2 + \sqrt{2 (1 + \cos 4 θ)}} = \sqrt{2 + \sqrt{2 . 2 \cos^{2} 2 θ}} = \sqrt{2 + 2 \cos 2 θ} = \sqrt{2 (1 + \cos 2 θ)} = \sqrt{2 . 2 \cos^{2} θ} = 2 \cos θ = RHS

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