Question

How do i find the exact value of sin 15 using the half angle formula

Answer 1

sin (30/2) = +/- sqrt [(1-cos 30)/2]
+ in first quadrant

= sqrt [ (1 - {sqrt 3}/2)/2) ]

= sqrt [ (2 - sqrt 3)/4 ]

= (1/2) sqrt (2 - sqrt 3)

Answer 2

use
cos 2A = 1 - 2sin^2 A
cos 30° = 1 - 2sin^2 15°
√3/2 = 1- 2sin^2 15°
2sin^2 15° - 1 - √3/2 = (2-√3)/2
sin^2 15° = (2-√3)/4

sin 15° = √(2-√3) /2

it would have been easier to do
sin15°
= sin(45°-30°)
= sin45cos30 - cos45sin30
= (√2/2)(√3/2) -(√2/2)(1/2)
= (√6 - √2)/4 which yields the same result as above