`cos A .cos B + sin A. sin B =?`

In a DeltaABC , if 4 cos A cos B + sin 2A+sin 2B+sin 2C=4 , then DeltaABC is

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

If A and B are complementary angles, prove that : cot A cot B - sin A cos B - cos A sin B = 0

If = 60^(@) and B=30^(@) , then show that : sin A cos B+ cos A sin B= sin (A+B)

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

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

Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.

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

In a DeltaA B C ,\ prove that , sin^3Acos(B-C)+sin^3B cos(C-A)+sin^3\ C cos(A-B) = 3\ sin A\ sin B \ sin C

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.