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Trigonometrical Equations
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यदि $\cos \theta + \cos 7\theta + \cos 3\theta + \cos 5\theta = 0$, तब $\theta =$
A
$\frac{{n\pi }}{4}$
B
$\frac{{n\pi }}{2}$
C
$\frac{{n\pi }}{8}$
D
इनमें से कोई नहीं
Solution
(c) $\theta $ व $7\theta $ तथा $3\theta $ व $5\theta $ को मिलाने पर,
$2\cos 4\theta (\cos 3\theta + \cos \theta ) = 0$
==> $4\cos 4\theta \,\cos 2\theta \cos \theta = 0$
==> $4\frac{1}{{{2^3}\sin \theta }}$ $(\sin {2^3}\theta ) = 0$; $\sin 8\theta = 0$.
$\therefore$ $\theta = \frac{{n\pi }}{8}$.
Standard 11
Mathematics
