if A+B=C and tanA=k tanB then prove that sin(A-B)=(k-1)/(k+1)sinC

Asked by Aarthi Vishwanathan | 1st Jun, 2012, 08:55: PM

Expert Answer:

tan A=k tanB ; or tan A\tan B=k

apply componendo & dividendo

(tan A -tanB)\(tanA+tanB)=(k+1)\(k-1)    

applying the identities

tan A tan B =sin (AB)\(cos A cosB)

sin(A-B)=(k-1).sinC\(k+1)

Answered by  | 1st Jun, 2012, 11:13: PM

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