If $(1 + \tan \theta )(1 + \tan \phi ) = 2$, then $\theta + \phi =$ ....$^o$
${30}$
${45}$
${60}$
${75}$
The number of values of $x$ in the interval $[0, 5 \pi ] $ satisfying the equation $3{\sin ^2}x - 7\sin x + 2 = 0$ is
The solution of the equation $cos^2\theta\, +\, sin\theta\, + 1\, =\, 0$ lies in the interval
$\tan \,{20^o}\cot \,{10^o}\cot \,{50^o}$ is equal to
Number of solutions of equation $sgn(sin x) = sin^2x + 2sinx + sgn(sin^2x)$ in $\left[ { - \frac{{5\pi }}{2},\frac{{7\pi }}{2}} \right]$ is
(where $sgn(.)$ denotes signum function) -
The equation $\sin x\cos x = 2$ has