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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)

Grade:11

2 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

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

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
11 Points
4 years ago
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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