SOLUTION: Find all solutions of the equation tan^2(x)=1-sec(x) and list all the solutions that are in the interval [0,2x)

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Question 741810: Find all solutions of the equation tan^2(x)=1-sec(x) and list all the solutions that are in the interval [0,2x)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find all solutions of the equation tan^2(x)=1-sec(x) and list all the solutions that are in the interval [0,2π)
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tan%5E2%28x%29=sec%28x%29
sin%5E2%28x%29%2Fcos%5E2%28x%29=1-1%2Fcos%28x%29
LCD%3Acos%5E2%28x%29
1-cos%5E2%28x%29=cos%5E2%28x%29-cos%28x%29
2cos%5E2%28x%29-cos%28x%29-1=0%29
(2cos(x)+1)(cos(x)-1)=0
2cos(x)+1=0
cos(x)=-1/2
x=2π/3,4π/3
or
cos(x)-1=0
cos(x)=1
x=0