Question

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

Answer 1

`\displaystyle x=\biggr\{(\pi)/(6),(11\pi)/(6)\biggr\}`

Explanation:

`\displaystyle 5\cos x-√(3)=3\cos x;\:0\leq x < 2\pi\\\\5-(√(3))/(\cos x)=3\\ \\-√(3)\sec x=-2\\\\\sec x=(2)/(√(3))\\\\\sec x=(2√(3))/(3)\\ \\\cos x=(3)/(2√(3))\\ \\\cos x=(3√(3))/(6)\\ \\\cos x=(√(3))/(2)\\\\x=\biggr\{(\pi)/(6),(11\pi)/(6)\biggr\}`