Prove that `cos^2 x + cos^2 3x + cos^2 5x + ....+` to n terms= 1/2 `[ n+ (sin4nx)/(2 sin2x)]`

Prove that cos^(2)x+cos^(2)3x+cos^(2)5x+....+ to nterms=1/2[n+(sin4nx)/(2sin2x)]

Prove that: cos^(2)2x-cos^(2)6x=sin4x sin8x

Prove that sin^(4)x-cos^(4)x=sin^(2)x-cos^(2)x

Prove that sin^(4)x-cos^(4)x=sin^(2)x-cos^(2)x

Prove that ( " cos " 4x + " cos " 3x + " cos " 2x)/(" sin " 4x + " sin " 3x + " sin " 2x) = " cot 3x

Prove that sin x + sin 3x + sin 5x + sin 7x=4 sin 4x cos 2x cos x.

Prove that: cos A cos 2A cos 2^(2)A cos 2^(3)A….....cos 2^(n-1)A=("sin" 2^(n)A)/(2^(n)"sin"A) .

sin x = 2 ^ (n) * cos (x) / (2) * cos (x) / (2 ^ (2)) * cos (x) / (2 ^ (3)) * ... * cos ( x) / (2 ^ (n)) * sin (x) / (2 ^ (n))