If α and β lie in first and second quadrants respectively and if sinα=1/2, sinβ=1/3 then find the value of sin(α+β)?

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If α and β lie in first and second quadrants respectively and if sinα=1/2, sinβ=1/3 then find the value of sin(α+β)?

sin(α+β)

=sinα.cosβ+cosα.sinβ

We know that 

sinα=1/2

cosα=√(1-sin^2α)=√(1-1/4)=√3/2

=sinα.cosβ+cosα.sinβ

=(1/2).(2√2/3)+(√3/2)(1/3)

=(√2/3)+(1/2√3)=(√2+1)/(3+2√3)

Hence the value of sin(α+β)=(√2+1)/(3+2√3)

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