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If sinalpha+sinbeta=a and cosalpha+cosbe...

If `sinalpha+sinbeta=a` and `cosalpha+cosbeta=b` prove that: `cos(alpha-beta)=((a^2+b^2-2)/2)`

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On squaring` sin alpha+ sin beta = a` and `cos alpha + cos beta = b` and adding them,
`sin^2alpha+sin^2beta+2sinalphasinbeta+cos^2alpha+cos^2beta+2cosalphacosbeta=a^2+b^2`
=`2+2sinalphasinbeta+2cosalphacosbeta=a^2+b^2`
=`2sinalphasinbeta+2cosalphacosbeta=a^2+b^2-2`
=`2cos(alpha-beta)=a^2+b^2-2`
=`cos(alpha-beta)=(a^2+b^2-2)/2`
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