Question

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)

Answer 1

Answer with explanation:

The given expression is:

`2 √(3)\cos x * \csc x+4 \cos x-3 \csc x-2√(3)\\\\=2 \cos x*(√(3)*\csc x+2)-√(3)*(√(3)*\csc x+2)\\\\\rightarrow (2\cos x -√(3))*(√(3)*\csc x+2)\\\\\rightarrow (2\cos x -√(3))*(√(3)*\csc x+2)=0\\\\(2\cos x -√(3))=0 \wedge (√(3)*\csc x+2)=0`

`\cos x=(√(3))/(2) \wedge \csc x=(-2)/(√(3))\\\\x=(\pi)/(6),2\pi-(\pi)/(6)\\\\x=(\pi)/(6),(11\pi)/(6) \wedge x=\pi+(\pi)/(3) ,2\pi-(\pi)/(3)\\\\x=(4\pi)/(3),(5\pi)/(3)\\\\x={(\pi)/(6),(11\pi)/(6),(4\pi)/(3),(5\pi)/(3)}`

Option C