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If $\cos \theta + \cos 2\theta + \cos 3\theta = 0$, then the general value of $\theta $ is
A
$\theta = 2m\pi \pm \frac{{2\pi }}{3}$
B
$\theta = 2m\pi \pm \frac{\pi }{4}$
C
$\theta = m\pi \pm {( - 1)^m}\frac{{2\pi }}{3}$
D
$(a)$ and $(b)$ both
Solution
$\cos \theta + \cos 2\theta + \cos 3\theta = 0$
==> $(\cos \theta + \cos 3\theta ) + \cos 2\theta = 0$
==> $2\cos 2\theta \cos \theta + \cos 2\theta = 0$
==> $\cos 2\theta (2\cos \theta + 1) = 0$
==> $\cos 2\theta = 0 = \cos \frac{\pi }{2}$
==> $\theta = \frac{\pi }{4}$
==> $\theta = 2m\pi \pm \frac{\pi }{4}$
or $\cos \theta = \frac{{ – 1}}{2} = \cos \frac{{2\pi }}{3}$
==> $\theta = 2m\pi \pm \frac{{2\pi }}{3}$.
Standard 11
Mathematics
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