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anonymous
 one year ago
Solve Trig Equation
\( tan^2 \theta = \frac{3}{2} sec \theta \)
anonymous
 one year ago
Solve Trig Equation \( tan^2 \theta = \frac{3}{2} sec \theta \)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sec ^2\theta\tan ^2\theta=1,\tan ^2\theta=\sec ^2\theta1\] \[\sec ^2 \theta1=\frac{ 3 }{ 2 }\sec \theta \] \[2 \sec ^2\theta2+3 \sec \theta=0\] solve further

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How did you get the top line?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So \( tan^2 \theta + 1 = sec^2 \theta \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is an identity \[\sin ^2\theta+\cos ^2\theta=1\] divide by \[\cos ^2\theta\] \[\tan ^2\theta+1=\sec ^2\theta\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok going to go solve I think I get it. BRB

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0solve by quadratic formula or by making factors.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[2 \sec ^\theta+4 \sec \theta\sec \theta2=0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0correction \[2 \sec ^2\theta\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok I am stuck I have sec = 1/2 and sec = 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[2\sec \theta \left( \sec \theta+2 \right)1\left( \sec \theta+2 \right)=0\] \[\left( \sec \theta+2 \right)\left( 2 \sec \theta1 \right)=0\] \[\sec \theta=2,\cos \theta=\frac{ 1 }{ 2 }=\cos \frac{ \pi }{ 3 }=\cos \left( \pi \pm \frac{ \pi }{ 3 } \right)=\cos \left( 2n \pi+\pi \pm \frac{ \pi }{ 3 } \right)\] \[\cos \theta=\cos \left\{ \left( 2 n+1 \right)\pi \pm \frac{ \pi }{ 3 } \right\}\] \[\theta=?\] or \[\sec \theta=\frac{ 1 }{ 2 },\cos \theta=2,rejected\] \[as~\left \cos \theta \right\le 1\]
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