Answer:
Therefore, x =240 °
[tex]\sin (x-210)=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given:
[tex]\tan x=\sqrt{3}[/tex] ..180° < x < 270°
To Find:
[tex]\sin (x-210) = ?[/tex]
Solution:
We Know that
[tex]\tan 60 =\sqrt{3}\\and\\\tan 240 =\sqrt{3}[/tex]
But given
[tex]\tan x=\sqrt{3}[/tex] ..180° < x < 270°
Therefore,
[tex]x = 240\°[/tex]
Now Substitute x in Sin ( x- 210°) we get
[tex]\sin (240-210)=\sin 30[/tex]
[tex]\sin 30 =\dfrac{1}{2}[/tex]
Therefore,
[tex]\sin (x-210)=\dfrac{1}{2}[/tex]
