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Prove that (cos alpha+ cos beta)^2+(sin...

Prove that `(cos alpha+ cos beta)^2+(sin(alpha)+sin beta)^2=4cos^2((alpha-beta)/2)`

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Given,`(cos alpha + cos beta)^2 + (sin alpha + sin beta)^2 = cos2alpha + cos2beta + 2 cos alpha cos beta + sin^2alpha + sin^2beta + 2 sin alpha sin beta`
= `(cos^2alpha + sin^2alpha) + (cos^2beta + cos^2beta) + 2(cos alpha cos beta + sin alpha sin beta)`
=` 1 + 1 + 2 cos(alpha – beta)`
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