General solution of frac{{tan ,2x, - ,tan ,x}}{{1, + ,tan ,x,tan ,2x}}, = ,1 is

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Trigonometrical Equations

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The general solution of $\frac{{\tan \,2x\, - \,\tan \,x}}{{1\, + \,\tan \,x\,\tan \,2x}}\, = \,1$ is

A

$\phi $

B

$n\pi \pm \frac{\pi }{3}$

C

$n\pi + \frac{\pi }{4}$

D

$n\pi + \frac{\pi }{6}\left( {n \in z} \right)$

Solution

$\frac{\tan 2 x-\tan x}{1+\tan x \tan 2 x}=\tan (2 x-x)=1$

${\tan x=1=\tan \frac{\pi}{4}} $

${x=n \pi+\frac{\pi}{4}}$

Standard 11

Mathematics

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