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

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

sin4A=4cos^(3)A sin A-4sin^(3)A cos A

Prove that: (cos2A+cos3A+cos4A)/(sin2A+sin3A+sin4A)= cot3A

Prove that: (cos^(3)A-cos3A)/(cosA)+(sin^(3)A+sin3A)/(sinA)=3

Prove that: (sin2A sin3A-sin4A sin5A+sin3A sin6A)/(cos2A cos3A-cos4A cos5A+cos3A cos6A)=tan A tan4A

Prove that sin 3x . sin^(3) x+cos 3 x . Cos^(3)x=cos^(3) 2x

Prove that: (sin3A+sin A)sin A+(cos3A-cos A)cos A=0