Prove that: `(cosalpha-cosbeta)^2+(sinalpha-sinbeta)^2=4sin^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[` Since, `cos (A-B)=cos A cos B+`
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