Prove that in any triangle ABC(i) `c^2 = a^2 + b^2-2ab cos C` (ii) `c=bcosA+acosB`

Prove that, in any triangle ABC, cos C=(a^2+b^2-c^2)/(2ab) .

Prove that, in any triangle ABC, cos B=(c^2+a^2-b^2)/(2ca) .

Prove in any triangle ABC that (i) a^(2)+b^(2)+c^(2)=2(bc cos A +ca cos B+ ab cos C) (ii) (b+c) cos A+(c+a)cos B+(a+b) cos C = a+b+c .

Prove that in a triangle ABC, bc cos A + ca cos B +ab cos C= 1/2(a^2+b^2+c^2)

Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2ab cos C .

In any triangle ABC, prove that : a (b cos C-c cos B) = b^2 -c^2 .

In triangle ABC , prove that c=acosB +bcosA .

In any triangle ABC, then by vectors, prove that : c^2=a^2+b^2-2ab cos C .

Prove in any triangle ABC that (i) a(cos B+cos C)=2(b+c) "sin"^(2)(A)/(2) (ii) a(cos C- cosB)= 2(b-c )"cos"^(2)(A)/(2)

Statement I: If in a triangle ABC, sin ^(2) A+sin ^(2)B+sin ^(2)C=2, then one of the angles must be 90^(@). Statement II: In any triangle ABC cos 2A+ cos 2B+cos 2C=-1-4 cos A cos B cos C