Which one of the following is true?

If $\alpha$ is a root of $25\cos^2\theta + 5\cos\theta - 12 = 0$ and $\pi/2 < \alpha < \pi$,then $\sin 2\alpha$ is equal to

If $\tan \theta \cdot \tan 2 \theta = 1,$ then the value of $\sin ^{2} 2 \theta + \tan ^{2} 2 \theta$ is equal to

Choose the $INCORRECT$ statement$(s)$.

To an observer on the ground,the angle of elevation of the top of a tower is $30^{\circ}$. If the height of the tower is $100 \ m$,find the distance between the top of the tower and the point of observation (in meters).

If $\cos A = m \cos B,$ then