Question

) Prove that tan3A-tan2A-tanA=tanAtan2A-tan2Atan3A-tan3Atana​

Answer 1

Step-by-step explanation:

lhs=tan3a-tan2a-tana

now, tan3a=tan(2a+a)

tan3a=tan2a+tana/1-tan2a tana. (since tan(a+b)= tana+tanb/1-tana tanb)

tan3a(1-tana tanb)=tan2a+tana

tan3a-tan3a×tana×tan2a=tan2a+tana

therefore, tan3a-tan2a-tana=tan3a×tan2a×tana

proved