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

Asked by BIPLAV BIJOY GOSWAMI | 27th May, 2013, 08:34: AM

Expert Answer:

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

Answered by  | 27th May, 2013, 04:20: PM

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