Question

True or False cos^2x=(1-cos2x)/2

Answer 1

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

Answer 2

False

(My answer on Apex was correct)