The value of $\frac{(\tan 69^{\circ} + \tan 66^{\circ})}{(1 - \tan 69^{\circ} \tan 66^{\circ})}$ is

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

If $180^{\circ} < \theta < 270^{\circ},$ then the value of $\sqrt{4 \sin^{4} \theta + \sin^{2} 2\theta} + 4 \cos^{2} \left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is

If $\cos A = \frac{3}{4}$,then $32\sin \left( \frac{A}{2} \right)\sin \left( \frac{5A}{2} \right) = $

$A$ telegraph post is bent at a point above the ground due to a storm. Its top just touches the ground at a distance of $10 \sqrt{3} \text{ m}$ from its foot and makes an angle of $30^{\circ}$ with the horizontal. Then,the height (in meters) of the telegraph post is:

If $x + y = 3 - \cos 4\theta$ and $x - y = 4 \sin 2\theta$,then: