Proving Equations using Euler's Identity

[roldy]

1. Use Euler's identity to prove that cos³(t)=3/4cos(t)+1/4cos(3t)



2. e^i\theta=cos(theta)+i*sin(theta)



3. 3/4cos(t)+1/2cos(3t)=3/4((e^it+e^-it)/2)+1/4((e^i3t+e^-i3t)/2)

 

[Pengwuino]

You might want to go the other route and figure out what cos(t)^3 is upon substituting the identity for cos(x).

 

[roldy]

Got it. Thanks a bunch. That was pretty simple, just overlooked the simple substitution.