Question

if 2tanA=3tanB,then prove that tan(A-B)=sin2B/(5-cos2B)

Answer 1

according to the given condition,

tanA = 3/2tanB.

putting this in the formula of tan(A-B) that is (tanA-tanB)/(1+tanA*tanB) we get,

(3/2*tanB - tanB)/(1+3/2*tan^2B)

or, (1/2tanB)*(2cos^2B)/(2cos^2B+3sin^2B)

or, (sinB*cosB)/(2cos^2B + 3sin^2B)

multiplying both the numerator and denominator by 2

we get, sin2B/(4cos^2B+6sin^2B)

or, sin2B/(4 + 2 sin^2B)

or, sin2B/(5 - cos2B). here we used the formula 1 - cos2B = 2sin^2B

Answer 2

very nice :) i was going about it a much more tedious way >.< lol

Answer 3

:D:D