Question

Solve: ✓3 cos x + sinx = ✓2.​

Answer 1

Step-by-step explanation:

$\sqrt{3} cosx + sinx = \sqrt{2} \\ 2(\frac{ \sqrt{3} }{2} cosx + \frac{1}{ 2 } \sin(x) ) \\ 2(sin \frac{\pi}{3} \cos(x) + cos \frac{\pi}{3} sinx) = \sqrt{2} \\ 2(sin( \frac{\pi}{3} + x)) = \sqrt{2} \\ sin(x + \frac{\pi}{3} ) = \frac{ \sqrt{2} }{2} \\ sin(x + \frac{\pi}{3} ) = \frac{1}{ \sqrt{2} } \\ \sin(x + \frac{\pi}{3} ) = \sin( \frac{\pi}{4} ) \\ \\ x + \frac{\pi}{3} = \frac{\pi}{4} \\ x = \frac{ - \pi}{12}$