Consider the expression 2√3 cos(x)csc(x)+4cos(x)-3csc(x)-2 √ 3 This expression can be represented as the product of the factors... _____ and _____By equating the expression to zero we get the solutions over the interval [0,2pi] as A: (pi/6, pi/3, 2pi/3 and 11pi/6)B: (5pi/6, 7pi/3, and 5pi/3) C: (pi/6, 4pi/3, 5pi/3, and 11pi/6)D: (pi/3, 2pi/3, 5pi/6, and 7pi/6)

Accepted Solution

Answer with explanation: The given expression is: Β [tex]2 \sqrt{3}\cos x * \csc x+4 \cos x-3 \csc x-2\sqrt{3}\\\\=2 \cos x*(\sqrt{3}*\csc x+2)-\sqrt{3}*(\sqrt{3}*\csc x+2)\\\\\rightarrow (2\cos x -\sqrt{3})*(\sqrt{3}*\csc x+2)\\\\\rightarrow (2\cos x -\sqrt{3})*(\sqrt{3}*\csc x+2)=0\\\\(2\cos x -\sqrt{3})=0 \wedge (\sqrt{3}*\csc x+2)=0[/tex] Β  [tex]\cos x=\frac{\sqrt{3}}{2} \wedge \csc x=\frac{-2}{\sqrt{3}}\\\\x=\frac{\pi}{6},2\pi-\frac{\pi}{6}\\\\x=\frac{\pi}{6},\frac{11\pi}{6} \wedge x=\pi+\frac{\pi}{3} ,2\pi-\frac{\pi}{3}\\\\x=\frac{4\pi}{3},\frac{5\pi}{3}\\\\x={\frac{\pi}{6},\frac{11\pi}{6},\frac{4\pi}{3},\frac{5\pi}{3}}[/tex]Option C