SOLUTION: tan^2(theta)-3sec(theta)+3=0 Solve for values on the unit circle in value of pi

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Question 750672: tan^2(theta)-3sec(theta)+3=0
Solve for values on the unit circle in value of pi
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
tan^2(theta)-3sec(theta)+3=0
Solve for values on the unit circle in value of pi.
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tan%5E2%28x%29-3sec%28x%29%2B3=0
%28sin%5E2%28x%29%2Fcos%5E2%28x%29%29-3%2Fcos%28x%29%2B3=0
LCD:cos^2(x)
sin%5E2%28x%29-3cos%28x%29%2B3cos%5E2%28x%29=0
1-cos%5E2%28x%29-3cos%28x%29%2B3cos%5E2%28x%29=0
1-3cos%28x%29%2B2cos%5E2%28x%29=0
2cos^2(x)-3cos(x)+1=0
(2cos(x)-1)(cos(x)-1)=0
..
2cosx-1=0
cosx=1/2
x=π/3, 5π/3 (in Q1 and Q4 where cos>0)
..
cosx-1=0
cosx=1
x=0