Double angle formula

Question

2cos^2pi/3-1 not sure how to solve this on the right

Answer 1

The identity says:

2cos²θ - 1 = cos 2θ. Your angle is pi/3 or 60°. That means the double angle is 2(pi/3) or 120°.

Given:

cos pi/3 = 1/2 (cos 60° = 1/2)

cos 2(pi/3) = cos (2pi/3) (cos 2(60°) = cos 120° = -1/2)

cos²θ = (cos θ)²

Checking the identity:

2cos²(pi/3) - 1 = cos 2(pi/3)

2(cos pi/3)² - 1 = cos (2pi/3)

2( 1/2 )² - 1 = -1/2

2( 1/4 ) - 1 = -1/2

1/2 - 1 = -1/2

-1/2 = -1/2