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

If $5 \sin \theta = 3$,find the numerical value of $\frac{\sec \theta - \tan \theta}{\sec \theta + \tan \theta}$.

If $\frac{\sin A - \sin C}{\cos C - \cos A} = \cot B,$ then $A, B, C$ are in

Two towers are situated at a certain distance apart. $A$ person observes the angle of depression of the top and bottom of the second tower from the top of the first tower as $30^{\circ}$ and $60^{\circ}$ respectively. If the height of the first tower is $60 \, m$,find the height of the second tower and the distance between the two towers. (in $m$)

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

If $\tan \theta - \cot \theta = 0$ and $\theta$ is a positive acute angle,then the value of $\frac{\tan (\theta + 15^{\circ})}{\tan (\theta - 15^{\circ})}$ is