SOLUTION: solve and name all the solutions of x tan^2x-secx=1

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Question 811748: solve and name all the solutions of x
tan^2x-secx=1
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
solve and name all the solutions of x
tan^2x-secx=1
***
tan%5E2%28x%29-sec%28x%29=1
sin%5E2%28x%29%2Fcos%5E2%28x%29-1%2Fcos%28x%29=1
LCD:cos^2(x)
sin%5E2%28x%29-cos%28x%29=cos%5E2%28x%29
1-cos%5E2%28x%29-cos%28x%29=cos%5E2%28x%29
2cos^2(x)+cos(x)-1=0
2cos(x)-1)(cos(x)+1)=0
..
2cos(x)-1=0
cos(x)=1/2
x=π/3+2πk, 5π/3+2πk, k=integer
or
cos(x)+1=0
cos(x)=-1
x=π+2πk, k=integer