Marked ques.

Dear Student ,

Please find below the solution to the asked query :

\frac{\sin 5 θ}{\sin θ} = \frac{\sin (2 θ + 3 θ)}{\sin θ} = \frac{\sin 2 θ \cos 3 θ + \cos 2 θ \sin 3 θ}{\sin θ} = \frac{2 \sin θ \cos θ (4 \cos^{3} θ - 3 \cos θ) + (2 \cos^{2} θ - 1) (3 \sin θ - 4 \sin^{3} θ)}{\sin θ} = \frac{\sin θ [2 \cos θ (4 \cos^{3} θ - 3 \cos θ) + (2 \cos^{2} θ - 1) (3 - 4 \sin^{2} θ)]}{\sin θ} = 8 \cos^{4} θ - 6 \cos^{2} θ + (2 \cos^{2} θ - 1) (3 - 4 (1 - \cos^{2} θ)) = 8 \cos^{4} θ - 6 \cos^{2} θ + (2 \cos^{2} θ - 1) (4 \cos^{2} θ - 1) = 8 \cos^{4} θ - 6 \cos^{2} θ + 8 \cos^{4} θ - 2 \cos^{2} θ - 4 \cos^{2} θ + 1 = 16 \cos^{4} θ - 12 \cos^{2} θ + 1 ANS . . . Correct optiion is A .

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