How do you use the half-angle identity to find the exact value of Cos(-22.5)?

1 Answer
Jun 21, 2018

cos(22.5)=2+22

Explanation:

cos (-22.5) = cos (22.5)
Use half angle identity:
cos(x2)=±1+cosx2
In this case,
x2=22.5, and x=45 --> cosx=cos45=22
cos(22.5)=±1+222=±2+22
Since cos (22.5) is positive, therefor,
cos(22.5)=2+22