Question

the gs of the equation tanx+tan4x+tan7x=tanxtan4xtan7x

Answer 1

Answer:

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Step-by-step explanation:

$Given \\ tanx+tan4x+tan7x=tan x \: tan4x \: tanx \\ \\</p><p>We \: know \: that \\\\ tan(a + b + c) \frac{tan(a) + tan(b) + tan(c) - tan(a)tan(b)tan(c)}{1 + tan(a)tan(b) + tan(b)tan(c) + tan(c)tan(a)} \\ \\</p><p> If \: a+b+c = n\pi,(n \: belongs to N ) \\ then \: tan(a+b+c)=0 \\\\ = >tana+tanb+tanc-tan(a)tan(b)tan(c) = 0 \\\\ =>tana+tanb+tanc=tan(a)tan(b)tan(c) \\\\ it \: is \: same \: as \: the \: given \: question = > \\ \\</p><p>Hence , x+4x+7x=n\pi \\ \\</p><p>=>12x=n \pi \\\\ = > x = \frac{n \pi}{12}$

$\large\boxed{ \fcolorbox{red}{blue}{hope \: it \: help \: you}}$