SOLUTION: solve for theta if 2 tan^2 theta + sec theta-4=0
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Question 277195: solve for theta if 2 tan^2 theta + sec theta-4=0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Recall that 
and that 
, hence:
LCD is 
so:
Now recall that 
so that 
and therefore:
\ +\ \cos\theta\ -\ 4\cos^2\theta\ =\ 0)
and finally:
Let 
, then
Which factors to:
\left(2x\ +\ 1\right)\ =\ 0)
or
Therefore:
or
And
\ \approx\ 0.841)
radians or 
radians
or
\ =\ \frac{2\pi}{3})
radians or 
radians.
Though you did not specify, I presumed you wanted the solutions on the interval 
John
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