The value of $\tan \left(57°\right) - \tan \left(12°\right) - \tan \left(57°\right)\tan \left(12°\right)$ is

• $\tan \left(69°\right)$

• $\tan \left(45°\right)$

• 0

• None of these

If a and b are two vectors of magnitude 2 inclined at an angle 60°, then the angle between a and a + b is

• 30°

• 60°

• 45°

• None of these

The angle of elevation of the Sun, when the shadow of the pole is $\sqrt{3}$ times the height of the pole, is

• 60°

• 45°

• 15°

• 30°

The curves x = y² and xy = k cut at right angles, if k² is equal to

• 1

• 0

• $\frac{1}{8}$

• 8

If $\sin \left(\mathrm{\theta }\right) \frac{\sqrt{3}}{2}$, then the general value of $\mathrm{\theta }$ is

• $\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{3}$

• $2\mathrm{n\pi } \pm \frac{\mathrm{\pi }}{6}$

• $2\mathrm{n\pi } \pm \frac{\mathrm{\pi }}{3}$

• $\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{6}$

The value of $\tan \left(9°\right) - \tan \left(27°\right) - \tan \left(63°°\right) + \tan \left(31°\right)$ is

• 3

• 2

• 8

• 4

If $\sin \left(\mathrm{\theta }\right) = \frac{1}{2}$ and where, $\mathrm{\theta }$ is an obtuse angle, then $\cot \left(\mathrm{\theta }\right)$ is equal to

• $- \frac{1}{\sqrt{3}}$

• $- \sqrt{3}$

• $\frac{1}{\sqrt{3}}$

• $\sqrt{3}$

A man is standing on the horizontal plane. The angle of elevation of top of the pole is $\mathrm{\alpha }$. If he walks a distance double the height of the pole, then the elevation of the pole is $2\mathrm{\alpha }$. The value of $\mathrm{\alpha }$ is

• $\frac{\mathrm{\pi }}{12}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{6}$

The value of sin(50°) cos (10°) + cos(50°) sin(10°) is

• $\frac{1}{2}$

• $\sqrt{3}$

• $\frac{\sqrt{3}}{2}$

• 1

160.

The least value of a, for which the function a $\frac{4}{\sin \left(\mathrm{x}\right)} + \frac{1}{1 - \sin \left(\mathrm{x}\right)}$ has at east one solution in the interval $\left(0, \frac{\mathrm{\pi }}{2}\right)$, is

• 9

• 4

• 5

• 1