[Math] Express $\sin 3\theta$ and $\cos 3\theta$ as functions of $\sin \theta$ and $\cos \theta$ using Euler’s identity

Question

Using Euler's identity ($e^{in\theta}=\cos n\theta+i \sin n\theta$), express $\sin 3\theta$ and $\cos 3\theta$ as functions of $\sin \theta$ and $\cos \theta$.

Any ideas?

Answer 1

HINT:

So, $$\cos3x+i\sin3x=e^{i3x}=(e^{ix})^3=(\cos x+i\sin x)^3$$

Use Binomial Expansion and equate the real & the imaginary parts