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

CBSE Class 11
1

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

2

Answer : Given : sinA + sinB =a and cosA + cos B=b
To find : the value of sin(A+B)
(sinA+sinB)2 = sin2A + 2sinAsinB + sin2B = b2
(cosA+cosB)2 =cos2A + 2cosAcosB + cos2B = c2
Using that 1 = sin2A+cos2A = sin2B+cos2B and adding you have:
1 + 2(sinAsinB+cosAcosB) + 1 = b2 + c2,
=> sin(A+B) = (sinAsinB+cosAcosB) = (b2+c2)/2 -1 Answer