- Home
- Standard 11
- Mathematics
Trigonometrical Equations
medium
$\sin 7\theta = \sin 4\theta - \sin \theta $ तथा $0 < \theta < \frac{\pi }{2}$ को सन्तुष्ट करने वाले $\theta $ के मान हैं
A
$\frac{\pi }{9},\frac{\pi }{4}$
B
$\frac{\pi }{3},\frac{\pi }{9}$
C
$\frac{\pi }{6},\frac{\pi }{9}$
D
$\frac{\pi }{3},\frac{\pi }{4}$
Solution
$\sin 7\theta + \sin \theta – \sin 4\theta = 0$
$ \Rightarrow $ $2\sin 4\theta \cos 3\theta – \sin 4\theta = 0$
$ \Rightarrow $ $\sin 4\theta (2\cos 3\theta – 1) = 0 $
$\Rightarrow \sin 4\theta = 0,\,{\rm{ }}\cos 3\theta = \frac{1}{2}$
अब $\sin 4\theta = 0$ $ \Rightarrow $ $4\theta = \pi $ $ \Rightarrow $ $\theta = \frac{\pi }{4}$
तथा $\cos 3\theta = \frac{1}{2}$ $ \Rightarrow $ $3\theta = \frac{\pi }{3}$ $ \Rightarrow $ $\theta = \frac{\pi }{9}$.
Standard 11
Mathematics
