[SOLVED] Solving Trigonometric equations 2

**mj.alawami** · March 24th 2009, 10:40 AM

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

**Opalg** · March 24th 2009, 01:32 PM

Originally Posted by mj.alawami

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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