trig
posted by lan on .
use a half angle formula to find the exact value of cos 75 degree

start with
cos 2A = 2cos^2 A  1
cos150° = 2 cos^2 75  1
√3/2 + 1 = 2cos^2 75°
cos^2 75° = (1  √3/2)/2
cos 75° = √[(1  √3/2)/2]
An easier ways would have been
cos75 = cos(45+30)
= cos45cos30  sin45sin30
= (1/√2)(√3/2)  (1/√2)(1/2)
= (√3  1)/(2√2)
Use your calculator to show that both produce cos75