Prove that : `cos^3 A cos 3A + sin^3 A sin 3A = cos^3 2A`

Prove that : cos^(3)A cos3A+sin^(3)A sin3A=cos^(3)2A

Prove the following : cos^3A.cos3A+sin^3Asin3A = cos^3 2A

Prove that cos ^ (3) and cos3e + sin ^ (3) and sin3e = cos ^ (3) 2e

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 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^(3) A + sin^(3) A)/ (cos A + sin A) + (cos^(3) A - sin^(3) A)/(cos A - sin A) = 2

Prove that (sin^3A+cos^3A)/(sin A+cos A)+(sin^3A-cos^3A)/(sin A-cos A)=2

Prove that (cos 3A +2 cos 5 A + cos 7A)/( cos A + 2 cos 3 A + cos 5A) = cos 2 A - sin 2 A tan 3 A.

Prove that, cos^(3) theta cos 3 theta + sin^(3) theta sin 3 theta = cos^(3) 2 theta

Prove that (sin A+cos A)(1-sin A cos A)=sin^(3)A+cos^(3)A