Using vector method prove that in any triangle `ABC ` ` a^2=b^2+c^2-2bc cos A`.

Prove that in triangle ABC , cos^(2)A + cos^(2)B + cos^(2)C lt 3/4 .

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

Prove that in triangle ABC,cos^(2)A+cos^(2)B-cos^(2)C=1-2sin A sin B cos C

In any triangle, ABC prove that: ac cos B-bc cos A=a^2-b^2

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 .

If cos A+cos B=4sin^(2)((C)/(2)) then prove that sides a,c,b of an triangle ABC in A.P.

In any triangle ABC, prove that: Delta=(b^(2)+c^(2)-a^(2))/(4cot a)

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

If in a triangle ABC, (bc)/(2 cos A) = b^(2) + c^(2) - 2bc cos A then prove that the triangle must be isosceless

In a Delta ABC if (a+b)cos((B)/(2))=b(a+c)cos((C)/(2)) then prove that the triangle ABC is isosceles.