Question

Prove that: tan3A tan2A tanA=tan3A-tan2A-tanA

Answer 1

3A=2A+A

putting tan both sides

tan 3A=tan(2A+A)

tan 3A=tan 2A+tanA/(1-tan2AtanA)

tan 3A(1-tan2AtanA)=tan2A+tanA

tan3A-tan3A×tan2A×tanA=tan2A+tanA

or

tan3A×tan2A×tanA=tan3A-tan2A-tanA

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Answer 2

Answer:

Step-by-step explanation:tan2A can be written as  tan(3A-A)

 

now we have tan(a-b)=tana-tanb/1+tanatanb

here a =2A & b=A

 

tan2A=tan(3A-A)=tan3A-tanA/1+tan3AtanA

 

tan2A(1+tan3Atan2A) = tan3A-tanA

 

tan2A + tan2Atan3AtanA = tan3A -tanA     or

 

     tan2Atan3AtanA = tan3A -tanA-tan2A

hence proved