Could you provide a proof of Euler’s formula: eiφ=cos(φ)+isin(φ)?

**Answer**

**Proof**:

Consider the function f(t)=e−it(cost+isint) for t∈R. By the product rule

f′(t)=e−it(icost−sint)−ie−it(cost+isint)=0

identically for all t∈R. Hence, f is constant everywhere. Since f(0)=1, it follows that f(t)=1 identically. Therefore, eit=cost+isint for all t∈R, as claimed.

**Attribution***Source : Link , Question Author : Jichao , Answer Author : Community*