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Trigonometrical Equations
easy
જો $\frac{{1 - \cos 2\theta }}{{1 + \cos 2\theta }} = 3$, તો $\theta $ નો વ્યાપક ઉકેલ મેળવો.
A
$2n\pi \pm \frac{\pi }{6}$
B
$n\pi \pm \frac{\pi }{6}$
C
$2n\pi \pm \frac{\pi }{3}$
D
$n\pi \pm \frac{\pi }{3}$
Solution
(d) $\frac{{1 – \cos 2\theta }}{{1 + \cos 2\theta }} = 3$
==> $\frac{{1 – (1 – 2{{\sin }^2}\theta )}}{{1 + (2{{\cos }^2}\theta – 1)}} = 3$
$ \Rightarrow $ ${\tan ^2}\theta = 3$
$ \Rightarrow $ $\theta = n\pi \pm \frac{\pi }{3}$.
Standard 11
Mathematics
