# [SOLVED] Solving Trigonometric equations

• March 24th 2009, 10:36 AM
mj.alawami
[SOLVED] Solving Trigonometric equations
Find the solution of the following equations if $0 \leq t \leq 2\pi$

$sec^2-2tant=0$

Attempt:
$(tant-2.3)(tant+0.4)$

Am I in the right track?(Wondering)

Thank you
• March 24th 2009, 11:42 AM
running-gag
I am afraid not

$\frac{1}{\cos^2 t}-2\frac{\sin t}{\cos t}=0$

$\frac{1-2\sin t \cos t}{\cos^2 t}=0$

$\frac{1-\sin 2t}{\cos^2 t}=0$

$\sin 2t = 1$ and $t \neq \frac{\pi}{2} + k \pi$

$2t = \frac{\pi}{2} + 2k \pi$

$t = \frac{\pi}{4} + k \pi$

$t = \frac{\pi}{4}$ or $t = \frac{5\pi}{4}$