Trigonometry - Mathematics Previous Year Questions

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45\(^\circ\). If flies off horizontally straight way from the point O. After one second, the elevation of the bird from O is reduced to 30\(^\circ\), then the speed (in m/s) of the bird is

Total number of solutions of \(\left| {\cot x} \right| = \cot x + {1 \over {\sin x}},x \in [0,3\pi ]\) is equal to

If \(\alpha,\beta,\gamma \in[0,\pi]\) and if \(\alpha,\beta,\gamma\) are in AP, then \({{\sin \alpha - \sin \gamma } \over {\cos \gamma - \cos \alpha }}\) is equal to

A tower \(T_1\) of the height \(60 \mathrm{~m}\) is located exactly opposite to a tower \(T_2\) of height \(80 \mathrm{~m}\) on a straight road. From the top of \(T_1\), if the angle of depression of the foot of \(T_2\) is twice the angle of elevation of the top of \(T_2\), then the width (in \(\mathrm{m}\)) of the road between the feet of the towers \(T_1\) and \(T_2\) is

The angles of a triangle are in the ratio $1: 2: 7$. The ratio of the greatest side to the least side is $(k+1):(k-1)$. The value of $k$ is