If `sinalpha-sinbeta=a` and `cosalpha+cosbeta=b` then write the value of `cos(alpha+beta)` .

Explanation

Given ,`sinalpha-sinbeta=a`..(1)
`cosalpha+cosbeta=b`...(2)

squaring and adding (1) and (2) we get

`(cos alpha + cos beta)^2 + (sin alpha - sin beta)^2=a^2+b^2`

=`cos^2 alpha + cos^2 beta + 2 cos alpha cos beta + sin^2alpha + sin^2beta - 2 sin alpha sin beta=a^2+b^2`



= `(cos^2alpha + sin^2alpha) + (cos^2beta + cos^2beta) + 2(cos alpha cos beta - sin alpha sin beta) =a^2+b^2`


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