How do I find all solutions in the interval [0, 2Pi):

Question

cotx=cscx-1

the answer choices are:
a.) x=Pi/2
b.) x=Pi/2 and 3Pi/2

Answer 1

pi/2 surely works, (try subbing it in)

remember that 3pi/2 is 270º

tan 270º is undefined, so cot 270º = 0
LS = cot 3pi/2 = 0
RS = 1/sin 270 - 1 = 1/-1 - 1 = -2
so 3pi/2 does not work.