SOLUTION: solve: sec^2(x)=(sqrt(3))tan(x)+1 on interval [0,pi)

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Question 655824: solve:
sec^2(x)=(sqrt(3))tan(x)+1
on interval [0,pi)
Answer by lwsshak3(11628) About Me  (Show Source):
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solve:
sec^2(x)=(sqrt(3))tan(x)+1
on interval [0,pi)
**
sec^2(x)=(sqrt(3))tan(x)+1
1/cos^2(x)=√3(sin(x)/cos(x))+1
LCD:cos^2(x)
1=√3sin(x)cos(x)+cos^2(x)
1-cos^2(x)=√3sin(x)cos(x)
sin^2(x)=√3sin(x)cos(x)
divide by sin(x)
sin(x)=√3cos(x)
sin(x)/cos(x)=√3
tan(x)=√3
x=π/3 (quadrant I where tan>0)