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Trigonometrical Equations
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यदि $\sec 4\theta - \sec 2\theta = 2$, तो $\theta $ का व्यापक मान है
A
$(2n + 1)\frac{\pi }{4}$
B
$(2n + 1)\frac{\pi }{{10}}$
C
$n\pi + \frac{\pi }{2}$or $\frac{{n\pi }}{5} + \frac{\pi }{{10}}$
D
इनमें से कोई नहीं
(IIT-1963)
Solution
(c) $\sec 4\theta – \sec 2\theta = 2$
$ \Rightarrow $ $\cos 2\theta – \cos 4\theta = 2\cos 4\theta \cos 2\theta $
$ \Rightarrow $ $ – \cos 4\theta = \cos 6\theta $
$ \Rightarrow $ $2\cos 5\theta \cos \theta = 0$
$\theta = n\pi + {\pi\over{2}}$ या $\frac{{n\pi }}{5} + \frac{\pi }{{10}}$.
Standard 11
Mathematics
