Prove that `a cos A + b cos B + c cos C = 4R sin A sin B sin C`

Prove that a cos A + b cos B + c cos C = 4 R sin A sin B sin C.

In any DeltaABC , prove that : a cos A + b cos B + c cos C = 2a sin B sin C

If A + B + C = pi then prove that cos A + cos B + cos C = 1 + 4 sin(A/2) .sin(B/2).sin(C/2)

If A + B + C = 180^@ , then prove that sin 2 A+ sin 2B + sin 2C = 4 sin A sin B sin C

If A+B+C=(3pi)/(2) , then show that cos 2A+cos 2B+cos 2C=1-4 sin A sin B sin C .

If A, B, C are interior angles of DeltaABC such that (cos A + cos B + cos C)^(2)+(sin A + sin B + sin C)^(2)=9 , then number of possible triangles is

If in a DeltaABC, (a cos A+b cos B+ c cos C)/(a sin B+b sin C+ c sin A)=(a+b+c)/(9R) , then prove that Delta is equilateral.

Let cos A + cos B + cos C = 0 and sin A + sin B + sin C = 0 then which of the following statement(s) is/are correct?

Prove that (cos A - cos B) ^(2) + (sin A - sin B ) ^(2) = 4 sin ^(2) ((A -B)/( 2 )).

In a Delta ABC , 2 sinA cos B + 2 sin B cos C + 2 sin C cos A = sin A + sin B + sin C, then Delta ABC is (a) Isoceles (b) Right Angled (c) Acute (d) None of these