If in a ` Delta A B C ,cos^2A+cos^2B+cos^2C=1,` prove that the triangle is right angled.

Explanation

It is given that `cos ^{2} {~A}+cos ^{2} {~B}+cos ^{2} {C}=1`, then,

`cos ^{2} {~A}+(1-sin ^{2} {~B})+cos ^{2} {C}=1`

`(cos ^{2} A-sin ^{2} B)+1+cos ^{2} C=1`

`1+cos (A+B) cos (A-B)+cos ^{2} C=1 `

`1+cos (180-C) cos (A-B)+cos ^{2} C=1`

`1-cos C cos (A-B)+cos ^{2} C=1`

`-cos C(cos (A-B)-cos C)=0`

`cos C(cos (A-B)-cos (180-(A+B)))=0`

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