Question

If tan⁡ x= root of 3, and 180°

Answer 1

`(1)/(2)`

Explanation:

If
`180^(\circ)<x<270^(\circ),` then angle
`x` is in the III quadrant.

Since
`\tan x=√(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)\\ \\=(1)/(2)`