The solution of $3\tan (A - {15^o}) = \tan (A + {15^o})$ is
$n\pi + \frac{\pi }{4}$
$2n\pi + \frac{\pi }{4}$
$2n\pi - \frac{\pi }{4}$
$\frac{{n\pi }}{2} + {( - 1)^n}\frac{\pi }{2}$
Find the principal solutions of the equation $\sin x=\frac{\sqrt{3}}{2}$
The number of real numbers $\lambda$ for which the equality $\frac{\sin (\lambda \alpha) \quad \cos (\lambda \alpha)}{\sin \alpha}=\lambda-1$,holds for all real $\alpha$ which are not integral multiples of $\pi / 2$ is
The equation $\sqrt 3 \sin x + \cos x = 4$ has
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 values of $x$ and $y$ which satisfy $\tan (x - y) = 1,\,$ $\sec (x + y) = \frac{2}{{\sqrt 3 }}$ are