SOLUTION: Im stuck. I need the exact solution from [o.2pi) tan^2(x)= 1-sec(x)

Question 1025159: Im stuck. I need the exact solution from [o.2pi)
tan^2(x)= 1-sec(x)
Found 2 solutions by richard1234, KMST:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Add 1 to both sides and use the identity

This is a quadratic in terms of sec x, which you can solve for. Remember that sec x = 1/cos x, and can only take on values whose absolute value is at least 1.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Using the trigonometric identities that we should all remember,
and ,
you can re-write the equation as
.
Multiplying both sides of the equal sign times ,
the equation above turns into
,
and since ,
you can substitute and re-write it as
<--> .
The last equation is a quadratic equation.
If you use , you can write it as

You can solve for using factoring, or completing the square, or the quadratic formula to get the solutions
.
In the interval ,
happens only for ,
while happens only for .

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