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if 2tanA=3tanB prove that

Asked by Mudita Agrawal 14th September 2013, 3:52 PM
Answered by Expert
Answer:
Given, tanA = 3/2tanB
 
Putting this in the formula of tan(A-B), we get,
tan (A - B) = (3/2*tanB - tanB)/(1+3/2*tan^2B)
= (1/2tanB)*(2cos^2B)/(2cos^2B+3sin^2B)
= (sinB*cosB)/(2cos^2B + 3sin^2B)
Multiplying both the numerator and denominator by 2 we get,
= sin2B/(4cos^2B+6sin^2B)
= sin2B/(4 + 2 sin^2B)
= sin2B/(5 - cos2B)
 
Hence, proved.
Answered by Expert 14th September 2013, 9:49 PM
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