Prove that :
`cos^2 A + cos^2 B - 2 cos A cos B cos (A+B) = sin^2 (A+B)`

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

If A + B + C =180^@ , prove that : cos^2 A+ cos^2 B+cos^2 C=1-2 cos A cos B cosC .

Prove that : 2cosA cosB = cos (A + B) + cos (A-B) .

If A + B + C =180^@ , prove that : cos^2 A- cos^2 B-cos^2 C=2 cos A sin B sinC -1 .

If A + B + C =360^@ , prove that : 1-cos^2 A-cos^2 B-cos^2 C+2 cos A cosB cos C=0 .

Prove that: (cos 2A cos 3A-cos 2A cos 7A + cos A cos 10A)/(sin 4A sin 3A -sin 2A sin 5A + sin 4A sin 7A)= cot 6A cot 5A .

Prove that : cos (A + B) = cos A cos B - sin A sin B .

Prove that : cos (A - B) = cos A cos B + sin A sin B .

Prove that : sin(A- B) = sin A cos B -cos A sin B .

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