If $A + B + C = 270^o,$ then $\cos 2A + \cos 2B + \cos 2C + 4\sin A \sin B \sin C = $

The angle of elevation of the top of an unfinished tower at a point $120\, m$ from its base is $45^{\circ}$. How much higher must the tower be raised so that its angle of elevation at the same point be $60^{\circ}$? (in $m$)

If $\frac{\sqrt{2} \sin \alpha}{\sqrt{1+\cos 2 \alpha}}=\frac{1}{7}$ and $\sqrt{\frac{1-\cos 2 \beta}{2}}=\frac{1}{\sqrt{10}}$ where $\alpha, \beta \in (0, \frac{\pi}{2})$,then $\tan (\alpha+2 \beta)$ is equal to

$\frac{\tan ^{2} \theta}{\sec \theta+1}-\sec \theta$ is equal to

If $(1+\tan ^{2} \theta)=\frac{625}{49}$ and $\theta$ is acute,then what is the value of $\sqrt{\sin \theta+\cos \theta}$?

If $\sec \theta(\cos \theta+\sin \theta)=\sqrt{2},$ then what is the value of $\frac{2 \sin \theta}{\cos \theta-\sin \theta} ?$