SOLUTION: Find all exact solutions on (0, 2pi) sec(x) sin(x) - 2 sin(x) = 0

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Question 1176502: Find all exact solutions on (0, 2pi)
sec(x) sin(x) - 2 sin(x) = 0

Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
sec x*sin x-2 sin x=0
sin x (sec x-2)=0
sin x=0, which would be at 0 and π.
sec x=2 which is same as cos x=(1/2), which is at π/3 and 5π/3
(π/3,π,5π/3) if literally the interval is (0, 2π). If the interval is [0, 2π) ,then 0 would be allowed
graph%28300%2C300%2C-1%2C7%2C-1%2C1%2C%28sin%28x%29%2Fcos%28x%29%29-2sin%28x%29%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find all exact solutions on (0, 2pi)
sec%28x%29%2Asin%28x%29+-+2sin%28x%29+=+0
%28sec%28x%29++-+2%29+%2Asin%28x%29+=+0

if
sin%28x%29+=+0

x=0,x=pi

or if
sec%28x%29+=+2............sec%28x%29+=1%2Fcos%28x%29
1%2Fcos%28x%29=2
cos%28x%29=1%2F2
x=cos%5E-1%281%2F2%29

x+=+pi%2F3, x+=+5pi%2F3