SOLUTION: how do you find the solutions for theta in this problem: 3 tan^2(theta) - 1 = sec^2(theta)

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Question 885074: how do you find the solutions for theta in this problem: 3 tan^2(theta) - 1 = sec^2(theta)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
how do you find the solutions for theta in this problem:
for interval: (0,2π)
3 tan^2(theta) - 1 = sec^2(theta)
3tan%5E2%28theta%29-1=sec%5E2%28theta%29
%283sin%5E2%28theta%29%29%2F%28cos%5E2%28theta%29%29-1=1%2Fcos%5E2%28theta%29
lcd: cos%5E2%28theta%29
3sin%5E2%28theta%29-cos%5E2%28theta%29=1
3sin%5E2%28theta%29-%281-sin%5E2%28theta%29%29=1
3sin%5E2%28theta%29-1%2Bsin%5E2%28theta%29=1
4sin%5E2%28theta%29=2
sin%5E2%28theta%29=%281%2F2%29
sin%28theta%29=±√(1/2)=±√2/2
theta= π/4, 3π/4, 5π/4, 7π/4