anonymous
  • anonymous
Find the general solution of tan2x = -cot(x+pie/3)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
u kno tan2x = 2tanx/1-tan^2x nd cotx = 1/tanx
anonymous
  • anonymous
form a quadratic nd solve........ for tanx........ then u l get the g.s
anonymous
  • anonymous
\[\tan(2x) = -\cot(90 + x -30) \implies -(-\tan(x-30)) = \tan(x - \frac{\pi}{6})\] \[\implies \tan(2x) = \tan(x - \frac{\pi}{3})\]

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More answers

anonymous
  • anonymous
General solution is given by: \[\tan ( \theta) = \tan(x)\] then: \[\theta = n \pi + x\]
anonymous
  • anonymous
so: \[2x = n \pi + ( x - \frac{\pi}{3} ) \implies x = n \pi + \frac{\pi}{3}\]
anonymous
  • anonymous
hey @waterineyes but my books says it as x = n pie + 5pie/6
anonymous
  • anonymous
So put n = 0 1 2 3 4 etc etc and find the corresponding value of x..
anonymous
  • anonymous
you can subtract it from \(2 \pi\)..
anonymous
  • anonymous
wat???
anonymous
  • anonymous
Wait something got wrong.. Let me check..
anonymous
  • anonymous
@w\ r uthere
anonymous
  • anonymous
Wait I am checking it..
anonymous
  • anonymous
I got it..
anonymous
  • anonymous
|dw:1343210793286:dw|
anonymous
  • anonymous
\[\tan(2x) = \cot(-x-60) \implies \cot(90 - (x + 150)) \implies \tan(x + 150)\] \[\tan(2x) = \tan(x + 150)\]
anonymous
  • anonymous
150 is in degrees: \[150^{\circ} = \frac{5 \pi}{6}\]
anonymous
  • anonymous
So: \[2x = n \pi + x + \frac{5 \pi}{6}\]
anonymous
  • anonymous
wat the wrong in 1 st method!!
anonymous
  • anonymous
and subtract x from both sides: \[x = n \pi + \frac{5 \pi}{6}\]
anonymous
  • anonymous
My mistake in reading i read as : x - pie/3
anonymous
  • anonymous
thxxx
anonymous
  • anonymous
Welcome dear..

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