If $\sin 5x + \sin 3x + \sin x = 0$, then the value of $x$ other than $0$ lying between $0 \le x \le \frac{\pi }{2}$ is
$\frac{\pi }{6}$
$\frac{\pi }{{12}}$
$\frac{\pi }{3}$
$\frac{\pi }{4}$
Number of values of $x$ satisfying $2sin^22x = 2cos^28x + cos10x$ in $x \in \left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right]$ is-
If $0 \le x \le \pi $ and ${81^{{{\sin }^2}x}} + {81^{{{\cos }^2}x}} = 30$, then $x =$
The equation $5x^2+12x + 13 = 0$ and $ax^2+bx + c = 0$ have a common root, where $a,b,c$ are the sides of $\Delta ABC$,then find $\angle C$ ? .....$^o$
Let $S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }$ If $T =\sum_{\theta \in S } \cos 2 \theta$, then $T + n ( S )$ is equal
The values of $\theta $ satisfying $\sin 7\theta = \sin 4\theta - \sin \theta $ and $0 < \theta < \frac{\pi }{2}$ are