Question

If $cos3\theta =cos3\alpha$, then the value of $\sin \theta$ can be given by

• A. $\pm \sin \alpha$
• B. $\sin (\frac{\pi }{3}\pm \alpha )$
• C. $\sin (\frac{2\pi }{3}+\alpha )$
• D. $\sin (\frac{2\pi }{3}-\alpha )$

Answer 1

Answer: (A), (C), (D)

$\pm \sin \alpha$
$\sin (\frac{2\pi }{3}+\alpha )$
$\sin (\frac{2\pi }{3}-\alpha )$

Given, $\cos 3\theta =\cos 3\alpha$
Therefore general solution can be given as,
$\Rightarrow 3\theta =2n\pi \pm 3\alpha$, where $n\in Z$
$\Rightarrow \theta =\frac{2n\pi }{3}\pm \alpha$
$\Rightarrow \sin \theta =\sin (\frac{2n\pi }{3}\pm \alpha )$
Hence option A, C and D are correct choices corresponding to $n=0$ and $n=1$