trigonometry - Use of de Moivre's Theorem and Euler's formula to solve an expression

Let $n$ be a natural number, the Show that

$$(\cos(2)+i\sin(2)+1)^n=2^{n}\cos^n(1)(\cos(n)+i\sin(n))$$

The use of Euler's formula and de Moivre's Theorem isn't succeeding. Does anyone have a hint for how I should proceed?

EDIT: Thank you all. There was a typo in the textbook, which is why I was struggling.

Answer

$$2^n\cos^n(1)(\cos(n)+i\sin(n))=2^n\cos^n(1)(\cos(1)+i\sin(1))^n =(2\cos(1)\cos(1)+i2\cos(1)\sin(1))^n=(2\cos^2(1)+i\sin(2))^n=(\cos(2)+i\sin(2)+1)^n$$