In a right-angled triangle the hypotenuse is $2\sqrt{2}$ times the perpendicular drawn from the opposite vertex. Then the other acute angles of the triangle are
 

If $\cos \alpha +\cos \beta =a,\sin \alpha +\sin \beta =b$ and $\alpha -\beta =2\theta ,$ then $\frac{\cos 3\theta }{\cos \theta }$ is equal to

The number of all possible triplets $\left(a_1,a_2,a_3\right)$ such that $a_1+a_2\cos 2x+a_3{\sin }^{2}x=0$ for all $x$ is :

If $A+B+C=\frac{3\pi }{2}$, then $\cos 2A+\cos 2B+\cos 2C$ is equal to