I would like to compute $\cos(5\theta)$ and $\sin(5\theta)$. I can use the formula $\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$ and $\sin(a+b)=\sin(a)\cos(b)+cos(a)\sin(b)$ but it's a little bit to long. Is there an other way to compute it ?
[Math] How compute $\cos(5\theta)$ and $\sin(5\theta)$
trigonometry
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Best Answer
Hint :
By Moivre formula:
$$\cos(5\theta)+i\sin(5\theta)=(\cos \theta+i\sin\theta)^5.$$
Then use binomial formula to compute $(\cos \theta+i\sin\theta)^5$ and conclude.