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if sinA+sinB=a, cosA+cosB=b prove that sin(A+B)=2ab/a^2+b^2

if sinA+sinB=a, cosA+cosB=b prove that sin(A+B)=2ab/a^2+b^2

Grade:11

1 Answers

Shailendra Kumar Sharma
188 Points
6 years ago
SinA+SinB=a
CosA+CosB=b

Now a2+b2 = Sin2A+Cos2A+2SinACosA+Sin2B+Cos2B+2SinBCosB
a2+b2-2=2(SinACosB+CosASinB)
Sin(A+B)=(a2+b2-2)/2
 

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