Solve tanx+tan2x+tan3x=tanxtan2xtan3x
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x+2x=3x
apply tan on both sides
we get,
tan(x+2x)=tan3x
tanx+tan2x/1-tanxtan2x=tan3x
tan x+ tan 2x= -tan 3x(tan xtan2x-1)
tan x+tan 2x=tanxtan2xtan3x-tan3x
therefore,
tanx + tan 2x +tan3x=tanx tan2x tan3x
apply tan on both sides
we get,
tan(x+2x)=tan3x
tanx+tan2x/1-tanxtan2x=tan3x
tan x+ tan 2x= -tan 3x(tan xtan2x-1)
tan x+tan 2x=tanxtan2xtan3x-tan3x
therefore,
tanx + tan 2x +tan3x=tanx tan2x tan3x
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