If sinA + sinB =a and cosA + cos B=b then what is value of sin(A+B)?

**Answer :** Given : sinA + sinB =a and cosA + cos B=b

**To find :** the value of sin(A+B)

(sinA+sinB)^{2} = sin^{2}A + 2sinAsinB + sin^{2}B = b^{2}

(cosA+cosB)^{2} =cos^{2}A + 2cosAcosB + cos^{2}B = c^{2}

Using that 1 = sin^{2}A+cos^{2}A = sin^{2}B+cos^{2}B and adding you have:

1 + 2(sinAsinB+cosAcosB) + 1 = b^{2} + c^{2},

=> sin(A+B) = (sinAsinB+cosAcosB) = (b^{2}+c^{2})/2 -1 Answer