Sunday, April 23, 2017

trigonometry - Proving that fracsinalpha+sinbetacosalpha+cosbeta=tanleft(fracalpha+beta2right)

Using double angle identities a total of four times, one for each expression in the left hand side, I acquired this.




sinα+sinβcosα+cosβ=sin(α2)cos(α2)+sin(β2)cos(β2)cos2(α2)sin2(β2)



But I know that if α and β are angles in a triangle, then this expression should simplify to



tan(α+β2)



I can see that the denominator becomes cos(α+β2)



But I cannot see how the numerator becomes




sin(α+β2)



What have I done wrong here?

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