If $(1 + \tan \theta )(1 + \tan \phi ) = 2$, then $\theta + \phi =$ ....$^o$
${30}$
${45}$
${60}$
${75}$
The set of values of $x$ for which the expression $\frac{{\tan 3x - \tan 2x}}{{1 + \tan 3x\tan 2x}} = 1$, is
The solution of the equation $cos^2\theta\, +\, sin\theta\, + 1\, =\, 0$ lies in the interval
The number of values of $x$ for which $sin2x + sin4x = 2$ is
The number of solutions of equation $3cos^2x - 8sinx = 0$ in $[0, 3\pi]$ is
If ${\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0$, then the general value of $\theta $ is