Answer:
-2+sqrt(3)
Explanation:
When cos(angle)=sqrt(3)/2
then sin(of that angle)= + or - 1/2 depending on the quadrant
Anyways 330 degrees is in the 4 quadrant. Cosine is positive there while sine is negative.
so sin(330)=-1/2
Formula for tan(x/2)=(1-cos(x))/sin(x)
Therefore tan(165)=tan(330/2)=(1-cos(330))/sin(330)=(1-sqrt(3)/2)/(-1/2)
Multiply top and bottom by 2 to get
tan(165)=(2-sqrt(3))/-1
tan(165)=-2+sqrt(3)