3sinA+4cosB=6...(i) 4sinB+3cosA=1...(ii) On adding Eqs.(i) and (ii) after taking square, (9sin2A+24sinA⋅cosB+16cos2B)+(16sin2B+24sinB⋅cosA+9cos2A)=37 ⇒9(sin2A+cos2A)+16(cos2B+sin2B)+24sin(A+B)=37 ⇒9+16+24sin(A+B)=37 ⇒24sin(A+B)=12 ⇒sin(A+B)=