Find all solutions of the equation in the interval 0 2 pi co

Find all solutions of the equation in the interval [0, 2 pi). cot^2x - 3 csc x = - 3 Write your answer in radians in terms of pi. If there is more than one solution, separate them with commas.

Solution

cot^2 x -3 cscx=-3

cot^2 x= csc^2 x -1

csc^2 x -1 -3 csc x=-3

csc ^2 x -1 -3cscx+3=0

csc^2x -3cscx +2=0

(cscx-1)(cscx-2)=0

cscx=1 and csc x=2

x=pi/2 and x= pi/6 ,5pi/6