Question

find the value of tan 3A - tan 2A - tan A

Answer 1

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

Answer 2

Answer:

tan2A

Step-by-step explanation:

tan3A - tan2A - tanA = tanA.tan2A.tan3A

tan3A - tanA = tan3A.tan2A.tanA + tan2A

tan3A - tanA = tan2A(tan3A.tanA + 1)

$\frac{tan3A - tanA}{1 + tan3A.tanA}$ = tan2A