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Trigonometrical Equations
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જો $\cos 7\theta = \cos \theta - \sin 4\theta $, તો $\theta $ નો વ્યાપક ઉકેલ મેળવો.
A
$\frac{{n\pi }}{4},\frac{{n\pi }}{3} + \frac{\pi }{{18}}$
B
$\frac{{n\pi }}{3},\frac{{n\pi }}{3} + {( - 1)^n}\frac{\pi }{{18}}$
C
$\frac{{n\pi }}{4},\frac{{n\pi }}{3} + {( - 1)^n}\frac{\pi }{{18}}$
D
$\frac{{n\pi }}{6},\frac{{n\pi }}{3} + {( - 1)^n}\frac{\pi }{{18}}$
Solution
(c) $\sin 4\theta = \cos \theta – \cos 7\theta $
==> $\sin 4\theta = 2\sin (4\theta )\sin (3\theta )$
$ \Rightarrow $ $\sin 4\theta = 0 $
$\Rightarrow $ $4\theta = n\pi $
or $\sin 3\theta = \frac{1}{2} = \sin \left( {\frac{\pi }{6}} \right)$
$ \Rightarrow $ $3\theta = n\pi + {( – 1)^n}\frac{\pi }{6} $
$\Rightarrow \theta = \frac{{n\pi }}{4},\,\frac{{n\pi }}{3} + {( – 1)^n}\frac{\pi }{{18}}$.
Standard 11
Mathematics
