Use a sum or difference identity to find an exact value sin(15 degrees)
The solution would
be like this for this specific problem:
30 + 15 = 45
sin 45 = sin(30+15) = sin30cos15 + cos30sin15
cos 45 = cos(30+15) = cos30cos15 - sin30sin15
sin45 = cos45 (= sqrt(2)/2)
sin30 = 1/2 and cos30 = sqrt(3)/2
1/2 cos15 + sqrt(3)/2 sin15 = sqrt(3)/2 cos15 - 1/2 sin15
(sqrt(3)/2 + 1/2)sin15 = (sqrt(3)/2 - 1/2)cos15
sin15 = (sqrt(3)/2 - 1/2)/(sqrt(3)/2 + 1/2) cos15
sin15 = (1/2 (sqrt(3) - 1))/(1/2 (sqrt(3) + 1) cos15
sin15 = (sqrt(3) - 1)/(sqrt(3) +1) cos15
cos15 = sin30/(2sin15) = 1/2/(2sin15) = 1/(4sin15)
sin15 = (sqrt(3) - 1)/(sqrt(3) + 1) (1/(4sin15))
4(sin15)^2 = (sqrt(3) - 1)/(sqrt(3) + 1)
4(sin15)^2 = (sqrt(3) - 1)^2 / ((sqrt(3) + 1)(sqrt(3) - 1))
4(sin15)^2 = (3 - 2sqrt(3) +1) / (3 - 1) = (4 - 2sqrt(3)) / 2 = 2 - sqrt(3)
sin15 = sqrt((2 - sqrt(3))/4)
sin15 = sqrt(2 - sqrt(3)) / 2
I am hoping that
this answer has satisfied your query and it will be able to help you in your
endeavor, and if you would like, feel free to ask another question.