Answer:
False
Step-by-step explanation:
From the trigonometric identity: cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y) we can get:
cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y)
cos(x+x) = cos(x)*cos(x) - sin(x)*sin(x)
cos(2x) = cos^2(x) - sin^2(x)
cos^2(x) = cos(2x) + sin^2(x) (eq. 1)
From the trigonometric identity: cos^2(x) + sin^2(x) =1 we can get:
cos^2(x) + sin^2(x) = 1
sin^2(x) = 1 - cos^2(x) (eq. 2)
Replacing equation (1) into equation (2) we get:
cos^2(x) = cos(2x) + 1 - cos^2(x)
cos^2(x) + cos^2(x) = 1 + cos(2x)
2*cos^2(x) = 1 + cos(2x)
cos^2(x) = [1+cos(2x)]/2
