Question

Tan70° = 2 Tan50° + Tan20° ....Prove that

Answer 1

tan (A+B) =( tanA +tanB)/(1-tanAtanB)

tan70 = tan(50+20)
= (tan50+tan20)/(1-tan50tan20)

tan70(1-tan50tan20)= tan50+tan20
tan70 - tan70tan50tan20 = tan50+tan20
tan 70 - tan(90-20)tan50tan20 = tan50+tan20
tan70 - cot20tan20 tan50 = tan50+tan20
tan70 - tan50 = tan50+tan20 [since tanx cotx = 1]

tan70 = tan50+tan50+tan20
tan70 = 2tan50+tan20