Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)

Question

csc²(x) + 2csc(x) - 3 = 0

I only got one answer which was π/2 + 2πn, but I don't understand how to find the other ones please help!

Answer 1

very nearly agree with Mark, but

csc(x)=-3, and csc=1 work exactly. 9-6-3=0 and 1+2-3=0-

need to add all x=sin^-1(-1/3)+2k*pi

and all x = pi-sin^-1(-1/3)+2k*pi=(2k+1)pi-sin^-1(-1/3)

Answer 2

csc² x + 2 csc x - 3 = 0

(csc x - 3)(csc + 1) = 0

csc x = 3

or

csc = -1