Question

√3cosx - sinx = √2 3√3 sinx + 3cosx = 3√3

Answer 1

$\sqrt{3} \cos(x) - \sin(x) = \sqrt{2} \\ 2( \frac{ \sqrt{3} }{2} \cos(x) - \frac{1}{2} \sin(x)) = \sqrt{2} \\ 2 \cos(x + \frac{\pi}{6} ) = \sqrt{2} \\ \cos(x + \frac{\pi}{6} ) = \frac{1}{ \sqrt{2} }$

x+π/6 = ±π/4 + 2πn

x = ±π/4-π/6+2πn

$\sqrt{3 } \sin(x) + 3 \cos(x) = 3 \sqrt{3} \\ 6( \frac{ \sqrt{3} }{2} \sin(x) + \frac{1}{2} \cos(x)) = 3 \sqrt{3} \\ \cos(x - \frac{\pi}{3} ) = \frac{ \sqrt{3} }{2}$

x-π/3 = ±π/6 + 2πk

x = ±π/6+π/3+2πk