Which of the following is the correct triple-angle identity for the cosine?

Test θ = 0°, where cos3θ = 1 and cosθ = 1: the four right-hand sides give 1, −1, −1 and 1, ruling out the middle two. Now test θ = 60°, where cos180° = −1 and cos60° = 1/2: the first gives $4(1/8)-3(1/2)=-1$ and the last gives $4(1/2)-3(1/8)=1.625$. Only cos3θ = 4co$s^3$θ − 3cosθ survives both tests.