SOLUTION: Solve for x in the equation 2sin xtan x + tan x - 2sin x - 1 = 0 for 0 = x =2π

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Question 195863: Solve for x in the equation 2sin xtan x + tan x - 2sin x - 1 = 0 for 0 = x =2π
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x in the equation 2sin%28x%29tan%28x%29+%2B+tan%28x%29+-+2sin%28x%29+-+1+=+0
for 0%3C=x%3C2pi 
 
2sin%28x%29tan%28x%29+%2B+tan%28x%29+-+2sin%28x%29+-+1+=+0

Factor tan%28x%29 out of the first two terms on the left:

tan%28x%29%282sin%28x%29+%2B+1%29+-+2sin%28x%29+-+1+=+0
        
Factor -1 out of the last two terms on the left:

tan%28x%29%282sin%28x%29+%2B+1%29-1%282sin%28x%29+%2B+1%29+=+0

Factor %282sin%28x%29%2B1%29 out of the left side:

%282sin%28x%29%2B1%29%28tan%28x%29-1%29+=+0

Set each factor = 0

2sin%28x%29%2B1=0%29        |tan%28x%29-1+=+0

2sin%28x%29=-1         |tan%28x%29+=+1

sin%28x%29+=+-1%2F2         |x+=pi%2F4, x+=+5pi%2F4
 
x=7pi%2F6, x=11pi%2F6

Solutions, smallest to largest:

pi%2F4, 7pi%2F6, 5pi%2F4, 11pi%2F6 

Edwin