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