Use a difference identity to find the exact value of sin15 degree.?

Answer 1

sin15° = sin(45 - 30)°
sin15° = sin 45° cos 30° - cos45° sin30°
sin15° = (1/√2)(√3/2) - (1/√2) (1/2)
sin15° = (1/(2√2) (√3 - 1)
sin15° = (√2/4)(√3 - 1)

Answer 2

Because of the unit circle, we know the value of all reference angles of 30 deg, 45 deg, 60 deg, and 90 deg. 15 deg can be solved for in two ways. One is difference, and the other is half angle. Half angle would be (30 deg / 2) and difference can be either (45 deg - 30 deg) or (60 deg - 45 deg)
You can use either, but I will use 45-30
sin(15)=sin(45-30)
sin(A−B) = sin A cos B − cos A sin B, so
sin(45−30) = sin 45 cos 30 − cos 45 sin 30
=√2/2 * √3/2 - √2/2 * 1/2
= √6/4-√2/4
=(6-√2)/4

Answer 3

use the identity is sin(a-b)=sin(a)cos(b)-sin(b)cos(a)
a-b=45-30
sin45cos30-sin30cos45
(root2/2 times root3/2)-(1/2 times root2/2)
root6/4-root2/4=(root6 - root2)/4

Answer 4

sin-345