Find the solution of the equation if $\displaystyle 0 \leq t \leq 2\pi $
Question
$\displaystyle tan^2t-sect=1 $
Attempt
$\displaystyle tan^2-\frac{1}{tant}-1=0 $
I have no idea what to do next?
Thank you
That's a reasonable attempt, but the problem is that if you multiply through by tan(t) then you'll have a cubic equation in tan(t), which doesn't look promising.
A better strategy would be to use the fact that $\displaystyle \tan^2t = \sec^2t-1$. Then the original problem becomes $\displaystyle \sec^2t - \sec t -2 = 0$. That's a quadratic in sec(t), which you should be able to solve.