Question

How do you find the exact values of tan 15° using the half angle formula?

Answer 1

tan 15= `-sqrt3 +2`

Explanation:

Use the formula `tan 2x= (2tan x)/ (1- tan^2 x)` with x= 15

tan 30 = `1/sqrt3 = (2tan 15)/(1-tan^2 15)`

`tan ^2 15 +2sqrt3 tan 15-1=0`

tan 15= `(-2sqrt3 +- sqrt (12 +4))/2`. Neglect negative value for x, as tan 15 would be positive in the 1st quadrant.

tan 15= `-sqrt3 +2`