SOLUTION: find all solutions: cscx + cotx = 1 ; in the interval [0,2pi)

Question 254929: find all solutions:
cscx + cotx = 1 ; in the interval [0,2pi)
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
find all solutions:
; in the interval [0,2pi)
first
csc(x) = 1/sin(x)
cot(x) = cos(x) / sin(x)
so we get

multiply by sin(x) to get

substituting, we get

squaring boh sides, we get

dividing by (1+cos(x)), we get

--
If x = pi/2,
then
csc(x) = 1 and cot(x) = 0; 1 + 0 = 1
if x = 3pi/2,
then
csc(x) = -1 and cot(x) = 0 ; -1 + 0 not = 1.
So it appear that our only answer is
X = PI/2.
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