Prove that: `(cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-beta)/2)`

Explanation

`L.H.S. ``=(cos alpha+cos beta)^{2}+(sin alpha-sin beta)^{2}`



`=(cos ^{2} alpha+cos ^{2} beta+2 cos alpha cos beta)+(sin ^{2} alpha+sin ^{2} beta+2 sin alpha sin beta)`




`=(cos ^{2} alpha+sin ^{2} alpha)+(cos ^{2} beta+sin ^{2} beta)+2(cos alpha cos beta+sin alpha sin beta)`



`=1+1+2[cos (alpha-beta)] quad`


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