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Trigonometrical Equations
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જો $\sin {\rm{ }}\left( {\frac{\pi }{4}\cot \theta } \right) = \cos {\rm{ }}\left( {\frac{\pi }{4}\tan \theta } \right)\,\,,$ તો $\theta = $
A
$n\pi + \frac{\pi }{4}$
B
$2n\pi \pm \frac{\pi }{4}$
C
$n\pi - \frac{\pi }{4}$
D
$2n\pi \pm \frac{\pi }{6}$
Solution
(a) We have $\frac{\pi }{4}\cot \theta = \frac{\pi }{2} – \frac{\pi }{4}\tan \theta $
$ \Rightarrow \tan \theta + \cot \theta = 2$
$ \Rightarrow $ $\sin 2\theta = 1 = \sin \frac{\pi }{2} $
$\Rightarrow \theta = n\pi + \frac{\pi }{4}$.
Standard 11
Mathematics
