The general value of $\theta $ satisfying ${\sin ^2}\theta + \sin \theta = 2$ is
$n\pi + {( - 1)^n}\frac{\pi }{6}$
$2n\pi + \frac{\pi }{4}$
$n\pi + {( - 1)^n}\frac{\pi }{2}$
$n\pi + {( - 1)^n}\frac{\pi }{3}$
If $2\,cos\,\theta + sin\, \theta \, = 1$ $\left( {\theta \ne \frac{\pi }{2}} \right)$ , then $7\, cos\,\theta + 6\, sin\, \theta $ is equal to
The number of solutions of the equation $\sin (9 x)+\sin (3 x)=0$ in the closed interval $[0,2 \pi]$ is
The number of solution of the given equation $a\sin x + b\cos x = c$ , where $|c|\, > \,\sqrt {{a^2} + {b^2}} ,$ is
The equation $3{\sin ^2}x + 10\cos x - 6 = 0$ is satisfied, if
The sides of a triangle are $\sin \alpha ,\,\cos \alpha $ and $\sqrt {1 + \sin \alpha \cos \alpha } $ for some $0 < \alpha < \frac{\pi }{2}$. Then the greatest angle of the triangle is.....$^o$