`4(b c*cos^2(A/2)+cos^2(B/2)+a b*cos^2(C/2))=(a+b+c)^2`

(iv) a^(2)(cos^(2) B - cos^(2)C) + b^(2) (cos^(2) C- cos^(2)A) + c^(2) (cos^(2)A- cos^(2)B)=0

If A+B+C=pi then prove cos( (A)/2) cos( (B-C)/2) + cos( B/2) cos((C-A)/2) + cos( C/2) cos( (A-B)/2) = sinA +sinB+sinC

In any Delta ABC, prove the following: (a+b+c)(cos A+cos B+cos C)=2((a cos^(2))(1)/(2)(A+b cos^(2))(1)/(2)(B+cos^(2))(1)/(2)C)

If A+B +C =2S, prove that : cos^2 S + cos^2 (S- A) + cos^2 (S-B)+ cos^2 (S -C) = 2 +2 cos A cos B cos C .

The expression cos^(2)(a+b+c)+cos^(2)(b+c)+cos^(2)a-2cos a*cos(b+c)cos(a+b+c) is indendent of

(a cos ^ (2) ((A) / (2)) + b cos ^ (2) ((B) / (2)) + c cos ^ (2) ((C) / (2))) / (a + b + c) <= (3) / (4)

If A+B-C=3pi,\ t h e n\ sin A+ sin B-sin C is equal to- a. 4sin(A/2)sin(B/2)cos(C/2) b. -4sin(A/2)sin(B/2)cos(C/2) c. \ 4cos(A/2)cos(B/2)cos(C/2) d. -4cos(A/2)cos(B/2)cos(C/2)

If A+B-C=3pi, t h e n sin A+ sin B-sin C is equal to- a.4sin(A/2)sin(B/2)cos(C/2) b. -4sin(A/2)sin(B/2)cos(C/2) c. 4cos(A/2)cos(B/2)cos(C/2) d. -4cos(A/2)cos(B/2)cos(C/2)

If A+B+C=(3pi)/(2) , prove that cos ^(2)A+ cos ^(2) B- cos ^(2)C=-2 cos A cos B sin C.