Verify cos^2x = (1+cos(2x))/2

Answer 1

cos²(x) = (1 + cos(2x))/2

cos²(x) = (1 + (2cos²(x) -1))/2 [replacing cos(2x) with the double angle identity cos(2x) = 2cos²(x) – 1]

cos²(x) = (2cos²(x))/2 [combining the +1 and -1]

cos²(x) = cos²(x) [canceling the 2's]