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Find the general solution of tan2x = cot(x+pie/3)?



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A.Avinash_Goutham
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u kno tan2x = 2tanx/1tan^2x nd cotx = 1/tanx

A.Avinash_Goutham
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form a quadratic nd solve........ for tanx........ then u l get the g.s

waterineyes
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\[\tan(2x) = \cot(90 + x 30) \implies (\tan(x30)) = \tan(x  \frac{\pi}{6})\]
\[\implies \tan(2x) = \tan(x  \frac{\pi}{3})\]

waterineyes
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General solution is given by:
\[\tan ( \theta) = \tan(x)\]
then:
\[\theta = n \pi + x\]

waterineyes
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so:
\[2x = n \pi + ( x  \frac{\pi}{3} ) \implies x = n \pi + \frac{\pi}{3}\]

Yahoo!
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hey @waterineyes but my books says it as x = n pie + 5pie/6

waterineyes
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So put n = 0 1 2 3 4 etc etc and find the corresponding value of x..

waterineyes
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you can subtract it from \(2 \pi\)..

Yahoo!
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wat???

waterineyes
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Wait something got wrong..
Let me check..

Yahoo!
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@w\ r uthere

waterineyes
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Wait I am checking it..

waterineyes
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I got it..

sauravshakya
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dw:1343210793286:dw

waterineyes
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\[\tan(2x) = \cot(x60) \implies \cot(90  (x + 150)) \implies \tan(x + 150)\]
\[\tan(2x) = \tan(x + 150)\]

waterineyes
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150 is in degrees:
\[150^{\circ} = \frac{5 \pi}{6}\]

waterineyes
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So:
\[2x = n \pi + x + \frac{5 \pi}{6}\]

Yahoo!
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wat the wrong in 1 st method!!

waterineyes
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and subtract x from both sides:
\[x = n \pi + \frac{5 \pi}{6}\]

waterineyes
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My mistake in reading i read as : x  pie/3

Yahoo!
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thxxx

waterineyes
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Welcome dear..