Question

Solve the equation on the
interval [0, 2π).
5 cos x - √3 = 3 cos x

Answer 1

Answer:

$\displaystyle x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}$

Step-by-step explanation:

$\displaystyle 5\cos x-\sqrt{3}=3\cos x;\:0\leq x < 2\pi\\\\5-\frac{\sqrt{3}}{\cos x}=3\\ \\-\sqrt{3}\sec x=-2\\\\\sec x=\frac{2}{\sqrt{3}}\\\\\sec x=\frac{2\sqrt{3}}{3}\\ \\\cos x=\frac{3}{2\sqrt{3}}\\ \\\cos x=\frac{3\sqrt{3}}{6}\\ \\\cos x=\frac{\sqrt{3}}{2}\\\\x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}$