Question

Solve $\sin x+\sqrt{3}.\cos x=\sqrt{2}$.

Answer 1

Solution

$sinx+\sqrt{3}cosx=\sqrt{2}$

$\frac{1}{2}sinx+\frac{\sqrt{3}}{2}cosx=\frac{1}{\sqrt{2}}$

$cos{60}^{\circ }sinx+sin{60}^{\circ }cosx=\frac{1}{\sqrt{2}}$

$sin(x+{60}^{\circ })=\frac{1}{\sqrt{2}}$

$x+\frac{\pi }{3}=2n\pi +\frac{\pi }{4},2n\pi +\frac{3\pi }{4}$

$x=2n\pi -\frac{\pi }{12},2n\pi +\frac{5\pi }{12}$