2.12.21 Asymptotic analysis

Condition: Write an asymptotic formula for a given \( f(x) \) for \( x \rightarrow a \), and the answer must contain at least two terms of the asymptotic formula, not counting the remainder. \[ f(x)=\sqrt{\frac{x}{x+1}}-\sqrt{\cos \frac{1}{x}}, \quad x \rightarrow \infty \]