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anonymous
 5 years ago
i need to solve this over the interval [0,2pi].
tan^2x=2secx1
anonymous
 5 years ago
i need to solve this over the interval [0,2pi]. tan^2x=2secx1

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i simplified tan^2x into sec^2x1. is that a good step?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(sec^2 x 1)  2 sec x +1 sec^2 x  2 sec x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sec (x)=u so substituting u^22u=0 We may complete the square by adding 1 to both side u^2 2u+1=1 (u1)(u1)=1 u=2 sec (x)=2 so since 1/sec(x)= cos(x) cos(x)=1/2 x=pi/3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I just define u for sec(x) for simplicity

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so is the work with sec(x)=u a continuation of the post you did before that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0U is used in place of sec(x), just to make it easier to see

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no, I did not need to use U. I could have instead solve it using sec(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Solved without using u sec(x)^22sec(x)=0 We may complete the square by adding 1 to both side sec(x)^2 2sec(x)+1=1 (sec(x)1)(sec(x)1)=1 sec(x)=2 sec (x)=2 so since 1/sec(x)= cos(x) cos(x)=1/2 x=pi/3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0could i have used the quadratic formula to solve from where it was secx^22secx=0?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and also how do you know you have to complete the square?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, but it is much easier

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0u^22u=0 I could see that by adding 1 to left side, I would be able to factor easily. But if you add something one one side, same must be done on the other side
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