Let $\tan \alpha = \frac{a}{a+1}$ and $\tan \beta = \frac{1}{2a+1}$,then $\alpha + \beta$ is

If $\cos (A-B)=3/5$ and $\tan A \tan B=2$,then which one of the following is true?

Evaluate: $\cos^2 48^\circ - \sin^2 12^\circ$

$\sin {163^\circ} \cos {347^\circ} + \sin {73^\circ} \sin {167^\circ} = $

If $\tan \theta = \frac{\cos 25^{\circ} + \sin 25^{\circ}}{\cos 25^{\circ} - \sin 25^{\circ}}$ and $\theta$ is in the third quadrant,then $\theta =$ (in $^{\circ}$)

If $\alpha$ is in the $3^{\text{rd}}$ quadrant,$\beta$ is in the $2^{\text{nd}}$ quadrant such that $\tan \alpha = \frac{1}{7}$ and $\sin \beta = \frac{1}{\sqrt{10}}$,then find the value of $\sin(2\alpha + \beta)$.