Half angle identities

Question

If , and  is in quadrant I, determine the exact value of each of the following. 

tan(x/2)=?

I got sin(x/2)= sqrt((9-sqrt(56))/18) and cos(x/2)= sqrt((9+sqrt(56))/18) but I can't figure out how to solve for tan (x/2)

Answer 1

If you have sin and cos, tan = sin / cos

half-angle problems often have more than one way to express the same number (using different radicals that don't immediately look like the same value). Another way to get the answer is the formula

tan x/2 = sin x / (1 + cos x)

= 5/9 / (1 + √(56)/9)