Question

If 2tanA=3tanB and tan(A-B) =sin2B÷ (k-cos2B) Then find the value of k?

Answer 1

hey frnd here ur best answer i hope its help full to u

an(A-B) = (tanA - tanB)/(1 + tanAtanB)

= (3/2 tanB - tanB)/(1 + 3/2 tanBtanB) ... given 2tanA = 3tanB

= tanB(3/2 - 1)/(1 + 3/2 tan2B)

= tanB (1/2)/(sec2B - tan2B + 3/2 tan2B) ..

since 1 + tan2B = sec2B

= tanB (1/2)/(sec2B + 1/2 tan2B)

= sinB cosB/(2 + sin2B)

= 2sinB cosB/(4 + 2sin2B)

= sin2B /(4 + 1 - cos2B)

.... 2sin2B = 1 - cos2B

= sin2B /(k- cos2B)

ans..

thnk you