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If sin alpha + sin beta = a and cos alp...

If `sin alpha + sin beta = a and cos alpha + cos beta =b`, show that `sin(alpha+beta)=(2ab)/(alpha^2+beta^2)`

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`Sin(alpha) + Sin(beta)=a` `Cos(alpha) + cos(beta)=b` `2Sin((alpha +beta)/2)Cos((alpha-beta)/2)=a` `2cos((alpha+beta)/2)cos((alpha-beta)/2)=b` then, `tan((alpha+beta)/2)= a/b`
By using angles of triangle,
`Sin((alpha+beta)/2)=a/sqrt(a^2+b^2)`
`cos((alpha+beta)/2)= b/sqrt(a^2+b^2)`
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