Question
1-2sin^2(theta/2)=2cos^2(theta/2)-1
Answers
Marth
To make it easier to type, let x = theta/2
1 - 2sin^2 (x) = 2cos^2 (x) - 1
1 - sin^2 (x) - sin^2 (x) = cos^2 (x) + cos^2 (x) - 1
Because sin^2 (x) + cos^2 (x) = 1:
1 - sin^2 (x) = cos^2 (x)
1 - cos^2 (x) = sin^2 (x)
cos^2 (x) - sin^2 (x) = cos^2 (x) - sin^2 (x)
1 - 2sin^2 (x) = 2cos^2 (x) - 1
1 - sin^2 (x) - sin^2 (x) = cos^2 (x) + cos^2 (x) - 1
Because sin^2 (x) + cos^2 (x) = 1:
1 - sin^2 (x) = cos^2 (x)
1 - cos^2 (x) = sin^2 (x)
cos^2 (x) - sin^2 (x) = cos^2 (x) - sin^2 (x)