Question

If 2 tan a = 3 tan B, then tan (a - b) =​

Answer 1

Holaa Mate

⏩Answer:

given 2tan a= 3tan B

tanA = 3/2tanB

Put this value of tan A in the formula of tan(A-B).

tan (A - B) = (tanA-tanB)/(1+tanA*tanB)

= (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)

(Using the formula 1 - cos2B = 2sin^2B)

Hence, proved.

Answer 2

Answer:

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