Question

If tan⁡ x= root of 3, and 180°

Answer 1

Answer:

$\dfrac{1}{2}$

Step-by-step explanation:

If $180^{\circ}$ then angle $x$ is in the III quadrant.

Since $\tan x=\sqrt{3},$ then $x=240^{\circ}\ [180^{\circ}+60^{\circ}]$ (we get angle in the III quadrant)

Consider $\sin (x-210^{\circ}).$

If $x=240^{\circ},$ then

$\sin (240^{\circ}-210^{\circ})\\ \\=\sin 30^{\circ}\\ \\=\dfrac{1}{2}$