For $a\sin \theta + b\cos \theta$, if $a=1, b=1$, the maximum occurs when $\theta = 45^\circ$ or $\pi/4$. Here $\theta = (x + 30^\circ)$. So, $x + 30^\circ = 45^\circ \implies x = 15^\circ$, which is $\pi/12$. Working in degrees can often be faster for mental math than manipulating $\pi$ fractions.