If 2tanB+cotB=tanA,prove that 2tan(A-B)=cotB

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Answer 1

If 2tanB+cotB=tanA,prove that 2tan(A-B)=cotB

 

2tan(A - B)

2{(tanA - tanB)/(1+tanA.tanB)}

now substitute for tanA = 2tanB + cot B,

2{(2tanB + cotB - tanB)/(1 + (2tanB + cotB).tanB)}

2{(tanB + cotB)/(2 + 2tan^2B)}   (using cotB*tanB = 1)

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

cotB{(tan^2B + 1)/(1 + tan^2B)}   (using cotB*tanB = 1)

cotB

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