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

-2+sqrt (3)

Step-by-step 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)