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Question

tanx+tan2x+tan3x=0 then x =

A
nπ+π3
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B
nπ+π4
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C
nπ or nπ±π3
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D
2nπ
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Solution

The correct option is B nπ or nπ±π3

LHS=sinxcosx+sin2xcos2x+sin3xcos3x

LCM of cosx and cos2x is taken,so
=sinxcos2x+cosxsin2xcosxcos2x+sin3xcos3x


=sin3xcosxcos2x+sin3xcos3x


sin3x=0 or cos3x+cosxcos2x=0
sin3x=0 or 2cos3x+2cosxcos2x=0
sin3x=0 or 2cos3x+cos3x+cosx=0
sin3x=0 or 3cos3x+cosx=0
sin3x=0 or 3(4cos3x3cosx)+cosx=0
x=nπ or x=nπ±π3


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