Question

If value of cos330° is √3/2 then find tan165°.

Answer 1

-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)