Question

if cot b=2tan(a-b), then find the value of tana+tanb+tana.tanb​

Answer 1

2tan(A-B)=2{tanA-tanB/1+tanAtanB}

Given:tanA=2tanB+cotB

2tanA=tanB+tanB+1/tanBtanA-tanB={(tan^2B+1)/(tanB)

From 2tanAtanB=2tan^2B+1

Substitute 3 and 4 in 1

You get2tan(A-B)=2

{tan^2B+1)/(tanB)/2tan^2B+2}2tan(A-B)

={(tan^2B+1)/(tanB)/tan^2B+1}2tan(A-B)

=(1/tanB)2tan(A-B)=cotB