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

Step-by-step explanation:

tan2A can be written as tan(3A-A)

We know that tan(a-b)=tana-tanb/1+tanatanb

Putting a =2A & b=A

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

tan2A(1+tan3Atan2A) = tan3A-tanA

tan2A + tan2Atan3AtanA = tan3A -tanA

tan2Atan3AtanA = tan3A -tanA-tan2A

Thus proved