If $\sin (A + B) =1 $ and $\cos (A - B) = \frac{{\sqrt 3 }}{2},$ then the smallest positive values of $A$ and $ B$ are
${60^o},{\rm{ }}{30^o}$
${75^o},{\rm{ }}{15^o}$
${45^o},{\rm{ }}{60^o}$
${45^o},{\rm{ }}{45^o}$
If the equation $2\ {\sin ^2}x + \frac{{\sin 2x}}{2} = k$ , has atleast one real solution, then the sum of all integral values of $k$ is
The smallest positive angle which satisfies the equation $2{\sin ^2}\theta + \sqrt 3 \cos \theta + 1 = 0$, is
The angles $\alpha, \beta, \gamma$ of a triangle satisfy the equations $2 \sin \alpha+3 \cos \beta=3 \sqrt{2}$ and $3 \sin \beta+2 \cos \alpha=1$. Then, angle $\gamma$ equals
No. of solution of equation $sin^{65}x\, -\, cos^{65}x =\, -1$ is, if $x \in (-\pi , \pi )$
The equation $3{\sin ^2}x + 10\cos x - 6 = 0$ is satisfied, if