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Trigonometrical Equations
easy
જો $\sin 2\theta = \cos 3\theta $ અને $\theta $ એ લઘુકોણ હોય તો $\sin \theta $ મેળવો.
A
$\frac{{\sqrt 5 - 1}}{4}$
B
$\frac{{ - \sqrt 5 - 1}}{4}$
C
$0$
D
એકપણ નહિ.
Solution
(a) $\sin 2\theta = \cos 3\theta $
$ \Rightarrow $ $3\theta = 2n\pi \pm \left( {\frac{\pi }{2} – 2\theta } \right)$
$ \Rightarrow $ $\theta = \frac{{2n\pi }}{5} + \frac{\pi }{{10}}$
or $\theta = 2n\pi – \frac{\pi }{2}$.
Since $\theta $ is acute
==> $\theta = \frac{\pi }{{10}}$
==> $\sin \theta = \frac{{\sqrt 5 – 1}}{4}$.
Standard 11
Mathematics
