If tan x + tan left( {frac{pi }{3} + x} right | vedclass

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Question

(c) $	an x + 	an \,\left( {\frac{\pi }{3} + x} ight) + 	an \,\left( {\frac{{2\pi }}{3} + x} ight)$

$ = 	an x + \frac{{	an x + \sqrt 3 }}{{

Vedclass · Accepted Answer

$	an 3x = 1$

Vedclass · Answer

(c) $	an x + 	an \,\left( {\frac{\pi }{3} + x} ight) + 	an \,\left( {\frac{{2\pi }}{3} + x} ight)$

$ = 	an x + \frac{{	an x + \sqrt 3 }}{{1 - \sqrt 3 \,	an x}} + \frac{{	an x - \sqrt 3 }}{{1 + \sqrt 3 \,	an x}}$

$ = 	an x + \frac{{8	an x}}{{1 - 3{{	an }^2}x}} $

$= \frac{{3\,(3	an x - {{	an }^3}x)}}{{1 - 3{{	an }^2}x}} = 3	an 3x$

Therefore, the given equation is 

$\Rightarrow$ $3	an 3x = 3$==> $	an 3x = 1.$

If $\tan x + \tan \left( {\frac{\pi }{3} + x} \right) + \tan \left( {\frac{{2\pi }}{3} + x} \right) = 3,$ then

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