If $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3},$ the value of $A + B$ is

If $\tan \alpha = \frac{x^2 - x}{x^2 - x + 1}$ and $\tan \beta = \frac{1}{2x^2 - 2x + 1}$ $(x \ne 0, 1)$,where $0 < \alpha, \beta < \frac{\pi}{2}$,then $\tan(\alpha + \beta)$ has the value equal to:

If $\theta$ is an acute angle and $\tan(4\theta - 50^{\circ}) = \cot(50^{circ} - \theta)$,then the value of $\theta$ in degrees is:

If $\theta$ lies in the second quadrant,then the value of $\sqrt{\frac{1 - \sin \theta}{1 + \sin \theta}} + \sqrt{\frac{1 + \sin \theta}{1 - \sin \theta}}$ is:

Without using trigonometric tables,evaluate: $\sin 48^{\circ} \sec 42^{\circ} + \cos 48^{\circ} \operatorname{cosec} 42^{\circ} = $

If $\cos \theta + \sin \theta = \sqrt{2} \cos \theta$,then $\cos \theta - \sin \theta =$