∵5cosx+12cosy=13 ⇒(5cosx+12cosy)2=169 ∴(5cosx+12cosy)2+(5sinx+12siny)2 ⇒(13)2+(5sinx+12siny)2 =25+144+120(sinxsiny+cosxcosy) ⇒(5sinx+12siny)2=120cos(x−y) ∵−1≤cos(x−y)≤1 ∴ Maximum value of 5sinx+12siny=√120