Outer measure equality proof

Question

I need your help with this.

Let (X,$\mathcal{A},\mu $) be a measure space.

$$\mu_1^*(E) = \inf\{{\sum \mu(A_i): E\subset \bigcup_i^\infty A_i, A_i \in \mathcal{A}, i \geq 1 }\},E \subset X\\ \mu_2^*(E) = \inf\{{\mu(A): E\subset A, A \in \mathcal{A} }\},E \subset X$$

I have to prove that $\mu^*_1$=$\mu^*_2$.