If $\cos 3 θ = \cos 3 α$ , then the value of sin $θ$ can be given by

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$\sin (\frac{2 π}{3} - α)$

$\pm \sin α$

$\sin (\frac{2 π}{3} + α)$

$\sin (\frac{π}{3} \pm α)$

answer is A, C, D.

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Detailed Solution

$\cos 3 θ = \cos 3 α$
Putting n = 0, 1, we have
$\begin{array}{ll} 3 α = 2 nπ \pm 3 α \\ ∴ 3 θ = 3 α or - 3 α or 2 π + 3 α or 2 π - 3 α \\ θ = α or - α or \frac{2 π}{3} + α or \frac{2 π}{3} - α \end{array}$
Hence, options (a), (c), (d) are correct
If $n = - 1, then 3 θ = - 2 π \pm 3 α$
$\Rightarrow θ = - \frac{2 π}{3} \pm α \begin{aligned} \Rightarrow \sin θ = \sin (- \frac{2 π}{3} \pm α) = - \sin (\frac{2 π}{3} \pm α) \\ = - \sin (π - \frac{π}{3} \pm α) = - \sin (\frac{π}{3} \pm α) \end{aligned}$
Hence, (b) is not correct.