Trigonometric Ratios And Identities - Trigonometry - Mathematics Previous Year Questions

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 upper \((\frac{3}{4})\) th portion of a vertical pole subtends an angel \(\tan ^{-1}\left(\frac{3}{5}\right)\) at a point in the horizontal plane through its foot and at a distance \(40 \mathrm{~m}\) from the foot. A possible height of the vertical is

If \(A, B, C \in[0, \pi]\) and if \(A, B, C\) are in \(\mathrm{AP}\), then \(\frac{\sin A+\sin C}{\cos A+\cos C}\) is equal to

If $A+B=\frac{\pi}{4}$, then $(1+\tan A)(1+\tan B)$ is equal to