if 2tanB + cotB = tanA then prove that: tanB = 2tan(A - B)

Question

SAGAR SINGH - IIT DELHI · Answer

Dear student,

2tanB+cotB=tanA

2tan^2B+1=tanAtanB

tan^2B=tanAtanB-1

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Sagar Singh

B.Tech, IIT Delhi

2tanB + cotB = tanA

then prove that:

tanB = 2tan(A - B)

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

Nita · Answer

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

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if 2tanB + cotB = tanA then prove that: tanB = 2tan(A - B)

if 2tanB + cotB = tanA

then prove that:

tanB = 2tan(A - B)

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