If $A + C = B,$ then $\tan A \tan B \tan C = $

If $A = \sin^2 x + \cos^4 x$,then for all real $x :$

$(\cos \alpha + \cos \beta )^2 + (\sin \alpha + \sin \beta )^2 = $

$\frac{\cot \theta - \operatorname{cosec} \theta + 1}{\cot \theta + \operatorname{cosec} \theta - 1}$ is equal to

If $\tan \theta + \cot \theta = 2$ and $0^{\circ} < \theta < 90^{\circ}$,then the value of $\theta$ is (in $^{\circ}$)

If $\tan \alpha$ equals the integral solution of the inequality $4x^2 - 16x + 15 < 0$ and $\cos \beta$ equals the slope of the bisector of the first quadrant,then $\sin(\alpha + \beta)\sin(\alpha - \beta)$ is equal to