If tany=Qsinx/P+Qcosx,then prove that tan(x-y)= Psinx/Q+Pcosx. Share with your friends Share 2 Neha Sethi answered this Given:tany=QsinxP+Q cosx⇒tanx-x-y=QsinxP+Q cosx⇒tanx-tanx-y1+tanx tanx-y=QsinxP+Q cosx⇒sinx-tanx-ycosxP+Q cosx=Qsinxcosx+sinx tanx-y⇒sinxP+Q cosx-tanx-yP+Q cosxcosx=Q sinxcosx+Qsin2x tanx-y⇒-tanx-yP+Q cosxcosx-Qsin2x tanx-y=Q sinxcosx-Psinx-Qsinx cosx⇒tanx-y-Pcosx-Qcos2x-Qsin2x=-P sinx⇒tanx-yPcosx+Qcos2x+sin2x=P sinx⇒tanx-yPcosx+Q=P sinx using: cos2x+sin2x=1⇒tanx-y=PsinxQ+PcosxHence proved. -1 View Full Answer