Trigonometry
If tan A = (xsinB/1-xcosB) and tanB= (ysinA/1-ycosA) , prove that (sinA/sinB)= x/y.
1 Answer
Sankalp Das
tanA=xsinB/(1-xcosB).......Cross multiply..... tanA-xcosBtanA=xsinB......X=tanA/(sinB+cosBtanA)......X=sinA/cosA{(sinBcosA+sinAcosB)}/cosA......On solving we get x=sinA/sin(A+B)...(1)...Similarly y=sinB/sin(B+A)....(2)....... Dividing (1)/(2) we get x/y=sinA/sinB
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