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sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>...

`sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)`

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Given,`sinalpha+sinbeta=a ,cosalpha+cosbeta=b`
Squaring and adding
`=>a^2+b^2=(sinalpha+sinbeta)^2+(cosalpha+cosbeta)^2`
`=>a^2+b^2=sin^2alpha+sin^2beta+2sinalphasinbeta+cos^2alpha+cos^2beta+2cosalphacosbeta`
`=>a^2+b^2=2+2cos(alpha−beta)...(1)`
Again multliplying both we get
`=>ab=(sinalpha+sinbeta)( cosalpha+cosbeta)` `=>ab=sinalphacosalpha+sinalphacosbeta+sinbetacosalpha+sinbetacosbeta`
...
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