Find all solutions of the equation in the interval 0 2 Enter

Find all solutions of the equation in the interval [0, 2). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) csc x + cot x = 3

Solution

cscx +cotx = 3

1/sinx + cosx/sinx = 3

(1+cosx)/sinx =3

Now ( 1+2cos^2(x/2) -1 )/2sin(x/2)cos(x/2) =3

cosx/2 = 3

cos(x/2) cannot be greater than1

So, No solution exists DNE