Evaluate trigonometric expressions - challenge problems

Consider the expression $\sin x+\sqrt{3}\cos x$‍. We want to combine the two terms and write the expression in the form $A\sin (x+\alpha )$‍, where $A$‍ and $\alpha$‍ are constants, and $0\le \alpha \le {\displaystyle \frac{\pi }{2}}$‍.

$A=$‍

$\alpha =$‍