## anonymous one year ago if 0 is less then theta less than 360 degrees solve sec^2+2sec(2theta)=0

1. amoodarya

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2. amoodarya

$\frac{1+2\cos \theta}{\cos^2\theta}=0\\1+2\cos \theta=0\\cos \theta =\frac{-1}{2}$

3. anonymous

@amoodarya can you explain where your getting the one? is that a formula?

4. amoodarya

$\sec \theta =\frac{1}{\cos \theta}$

5. anonymous

@amoodarya alright so how would you go about solving that then with everything applied?

6. anonymous

@amoodarya where would the 2sec(2theta) go in the formula? isn't it suppose to be at the bottom not top?

7. amoodarya

$\sec^2\theta +2\sec \theta=0\\ \frac{ 1 }{ \cos^2\theta }+2\frac{ 1 }{ \cos \theta }=0\\\frac{ 1 }{ \cos^2\theta }+2\frac{ \cos \theta }{ \cos^2 \theta }=0\\\frac{1+2 \cos \theta }{ \cos^2 \theta }=0\\1+2 \cos \theta=0\\ \cos \theta=\frac{-1}{2}$

8. anonymous

@amoodarya so the answer is -1/2 then? is there a way to check it?

9. amoodarya

check for what ?

10. anonymous

for -1/2

11. amoodarya

$\cos (\theta)=-0.5\\ \theta =\pm(\frac{2\pi}{3})+2k \pi$

12. anonymous

What does that mean exactly?

13. amoodarya

if you mean denominator goes to zero , you are in a right way but in your case , no problem $denominator \neq 0$

14. amoodarya

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15. anonymous

Ooohhhhh I see now haha thank you very much!!!