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Question

If tanx+tan(x+π3)+tan(x+2π3)=3,then

A
tanx=1
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B
tan2x=1
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C
tan3x=1
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D
None of these
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Solution

The correct option is B tan3x=1

The given equation can be written as

tanx+tanx+tan(π3)1tanxtan(π3)+tanx+tan(2π3)1tanxtan(2π3)=3

tanx+tanx+313tanx+tanx31+3tanx=3

tanx+(tanx+3)(1+3tanx)+(13tanx)(tanx3)13tan2x=3

tanx+8tanx13tan2x=3

tanx(13tan2x)+8tanx13tan2x=3

3(3tanxtan3x)13tan2x=33tan3x=3

tan3x=1


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