Question

Calculate cos 37.5 using a half angle identity

Answer 1

cos(θ/2) = ± √{[1 + cos(θ)] / 2}

37.5 is half of 75 , which is half of 150 ... cos(150º) = - √3 / 2

Answer 2

2 * 37.5 = 75
2*75 = 150
150 = 180-30
so sin 150= 1/2
and cos 150 = -.5 sqrt 3
so
sin 75 = sqrt [ (1 +.5 sqrt 3)/2 ]
cos 75 = sqrt [ (1 - .5sqrt 3)/2 ]
so
cos 37.5 = cos 75/2 = sqrt { [ 1 + sqrt [ (1 - .5sqrt 3)/2 ] /2 }