If $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$,then $\cos 2A = $

If $\frac{x}{\cos \alpha} = \frac{y}{\cos \left(\frac{2 \pi}{3} - \alpha\right)} = \frac{z}{\cos \left(\frac{2 \pi}{3} + \alpha\right)}$,then the value of $(x + y + z)$ is equal to

$\frac{\sin A+\sin 7 A+\sin 13 A}{\cos A+\cos 7 A+\cos 13 A} =$

Two ships leave a port from a point at the same time. One goes with a velocity of $3 \text{ km/h}$ along North-East making an angle of $45^{\circ}$ with the East direction and the other travels with a velocity of $4 \text{ km/h}$ along South-East making an angle of $15^{\circ}$ with the East direction. Then, the distance between the ships at the end of two hours is

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

If $A > B$ and $\tan A - \tan B = x$ and $\cot B - \cot A = y$,then $\cot (A - B) = $