anonymous
  • anonymous
Does 2sinxtanx = 3 === 2-2cos^2x over 2cosx=3?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[{2-2\cos^2x \over 2cosx}=3\]
.Sam.
  • .Sam.
You want to find the solution? or just proving?
anonymous
  • anonymous
prove and find the solution. But is 2sinxtanx equivalent to what I wrote?

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anonymous
  • anonymous
the answer to your question is if they're equivalent is no. cross out the leading 2 and it will be.
anonymous
  • anonymous
but that's not the route i'd take...
anonymous
  • anonymous
all yours sam..
.Sam.
  • .Sam.
\[\frac{2(1-\cos^{2}x)}{2cosx}=3\] \[\frac{(1-\cos^{2}x)}{cosx}=3\] \[1-\cos^{2}x=3cosx\] \[-\cos^{2}x-3cosx+1=0\]
.Sam.
  • .Sam.
No whole number solutions
anonymous
  • anonymous
Hmm Ok... But there should be... I think
.Sam.
  • .Sam.
Solution for that is \[x=\sin ^{-1}\left(\sqrt{\frac{3}{2} \left(\sqrt{13}-3\right)}\right)\approx 1.26319\] and \[x=-\sin ^{-1}\left(\sqrt{\frac{3}{2} \left(\sqrt{13}-3\right)}\right)\approx -1.26319\]
anonymous
  • anonymous
Won't it be 2sinxtanx = 3 => 2(sin^2x)/cosx = 3 => 2(1 - cos^2x)/cosx = 3 => 2 - 2cos^2x = 3cosx => 2cos^2x + 3cosx - 2 = 0 => (2cosx - 1)(cosx + 2) = 0 cosx = 1/2, cosx = -2 => Impossible => x = Pi/3, 2Pi - Pi/3 = 5Pi/3
.Sam.
  • .Sam.
The "2" canceled from start , the furthest you can get is sin(x) tan(x)=3
Callisto
  • Callisto
2sinxtanx is not the same as 2-2cos^x over 2cosx
anonymous
  • anonymous
Ok. Is it the same as 2-2cos^2x over cosx?
Callisto
  • Callisto
yes
anonymous
  • anonymous
Thank you :)
Callisto
  • Callisto
You're welcome.. I didn't help anyway...
anonymous
  • anonymous
@c How do you get from the ranges 0
anonymous
  • anonymous
@Callisto
Callisto
  • Callisto
|dw:1332668946826:dw| Very ugly drawing sorry. But from the graph, we can know there are 2 solutions for cosx =0.5 as you know the first one is 60 the second solution is in quadrant IV , which gives positive value for cosx (i meant it is like the quadrant I) and from cos (360 -x) = cos x, you can get the 2nd angle by 360 -x =60 Hmm.. is that your question?
anonymous
  • anonymous
Yes, thank you :)
Callisto
  • Callisto
you're welcome!

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