3sinA+4cosB=6 ...(i) and 4sinB+3cosA=1 ...(ii) Squaring Eqs. (i) and (ii), we get 9sin2A+16cos2B+24sinAcosB=36 ...(iii) 16sin2B+9cos2A+24sinBcosA=1 ...(iv) Adding Eqs. (iii) and (iv), we get 9(sin2A+cos2A)+16(sin2B+cos2B)+24(sinAcosB+cosAsinB)=37 ⇒25+24sin(A+B)=37 sin(A+B)=