Question : From an aeroplane just over of river, the angle of depression of two palm trees on the opposite bank of the river is found to be $60^{\circ}$ and $30^{\circ}$, respectively. If the breadth of the river is 400 metres, then the height of the aeroplane above the river at that

Question : From a tower 125 metres high, the angle of depression of two objects, which are in a horizontal line through the base of the tower, are $45^{\circ}$ and $30^{\circ}$ and they are on the same side of the tower. The distance (in metres) between the objects is:

Question : If $x=\sqrt3+\frac{1}{\sqrt3}$, then the value of $(x-\frac{\sqrt{126}}{\sqrt{42}})(x-\frac{1}{x-\frac{2\sqrt3}{3}})$ is:

Question : If $\theta$ is a positive acute angles and $\operatorname{cosec}\theta =\sqrt{3}$, then the value of $\cot \theta -\operatorname{cosec}\theta$ is:

Question : Find the value of $\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$.