if 2tanB + cotB = tanA

then prove that:

tanB = 2tan(A - B)

Dear student,

 

2tanB+cotB=tanA

2tan^2B+1=tanAtanB

tan^2B=tanAtanB-1

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

2tan(A-B)=2{tanA-tanB/1+tanAtanB}........1Given:tanA=2tanB+cotB.......2tanA=tanB+tanB+1/tanBtanA-tanB={(tan^2B+1)/(tanB)}.........3From 2tanAtanB=2tan^2B+1.........4Substitute 3 and 4 in 1You 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