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3.Trigonometrical Ratios, Functions and Identities
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જો $\sin \theta + \sin 2\theta + \sin 3\theta = \sin \alpha $અને $\cos \theta + \cos 2\theta + \cos 3\theta = \cos \alpha $, તો $\theta$ મેળવો.
A
$\alpha /2$
B
$\alpha $
C
$2\alpha $
D
$\alpha /6$
Solution
(a) $\sin \theta + \sin \,3\theta + \sin \,2\theta = \sin \,\alpha $
==> $2\sin 2\theta \cos \theta + \sin 2\theta = \sin \alpha $
==> $\sin 2\theta (2\cos \theta + 1) = \sin \alpha $…..$(i)$
Now $\cos \theta + \cos 3\theta + \cos 2\theta = \cos \alpha $
$2\cos 2\,\theta \cos \,\theta + \cos 2\theta = \cos \alpha $
$\cos 2\theta \,(2\cos \theta + 1) = \cos \alpha $…..$(ii) $
From $(i)$ અને $(ii), $
$\tan 2\theta = \tan \alpha $
==> $2\theta = \alpha $
==> $\theta = \alpha /2$.
Standard 11
Mathematics
