Question

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

Answer 1

Step-by-step explanation:

2tan B + cot B = tan A

cot B =tan A - 2 tan B

Cot A = 2tan(A-B.).......

Answer 2

Answer:ANSWER!!!!!

Step-by-step explanation:

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