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







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.
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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