2cos(в квадрате)х\2=1+cosx=cos2x

Question

2cos(в квадрате)х\2=1+cosx=cos2x

Answer 1

1/2 (x+x cos(2 x)) = cos(x)+1 = cos(2 x) x cos^2(x) = 2 cos^2(x/2) = 2 sin(pi/4-x) sin(x+pi/4) x/2-1/2 x sin^2(x)+1/2 x cos^2(x) = cos(x)+1 = cos^2(x)-sin^2(x)