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  .
|
|
|
