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Question

Find the value of
tan3A. tan2A. tanA

A
tan2A-tanA+tan3A
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B
tan2A+tanA+tan3A
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C
tan3A-tan2A-tanA
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D
tan3A+tan2A-tanA
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Solution

The correct option is C tan3A-tan2A-tanA
We know,

tan(x+y)=tanx+tany1tanx tany

tan3A=tan(2A+A)=tan2A+tanA1tan2A tanA

tan3A(1tan2AtanA)=tan2A+tanA

tan3Atan2AtanA=tan3Atan2AtanA

Hence, proved.

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