if an angle θ is divided into two paarts so that the ratio of thier tangents is k and x is the distance between the two parts,then sinx/sinθ is given bya)k/1-kb)k-1/k+1c)k-1/kd)k+1/k-1

Alpha=A/B
A-B=x. ; A=x+B
given: Tan A/ Tan B =k
Sin A/cos A*cos B/sin A=k
Sin A Cos B/Cos A sin B=k
Applying compendo dividendo rule
Sin A cos B+ cos A sinB/ sin A cos B-cosA sin B =k+1/k-1
Sin (A+B)/ sin (A-B)= k+1/k-1
doing reciprocal
Sin ( A-B)/sin (A+B)=k-1/k+1
Sin X. =k-1/k+1 sin alpha. ( since A=X+B)