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Math Help - [SOLVED] Solving Trigonometric equations 2

  1. #1
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    [SOLVED] Solving Trigonometric equations 2

    Find the solution of the equation if  0 \leq t \leq 2\pi
    Question
     tan^2t-sect=1

    Attempt
     tan^2-\frac{1}{tant}-1=0

    I have no idea what to do next?


    Thank you
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Find the solution of the equation if  0 \leq t \leq 2\pi
    Question
     tan^2t-sect=1

    Attempt
     tan^2-\frac{1}{tant}-1=0

    I have no idea what to do next?
    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 \tan^2t = \sec^2t-1. Then the original problem becomes \sec^2t - \sec t -2 = 0. That's a quadratic in sec(t), which you should be able to solve.
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