`cos ^(2) 2x -cos ^(2) 6x = sin 4x sin 8x`

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

sin ^(2) 6x - sin ^(2) 4x = sin 2x sin 10x

cos4x=1-8sin^(2)x cos^(2) x

Number of solutions of the equation cos^(4) 2x+2 sin^(2) 2x =17 (cos x + sin x)^(8), 0 lt x lt 2 pi is

Number of solutions of the equation sin^(4) x-cos^(2)x sin x + 2 sin^(2) x+sin x=0 in 0 le x le 3pi is ________.

The value of (cos^(4)x+cos^(2)x sin^(2) x + sin^(2)x)/(cos^(2)x+ sin^(2) x cos^(2) x + sin^(4)x) is ____________

(cos x- cos y) ^(2) + (sin x - sin y) ^(2) =4 sin ^(2) "" ( x-y)/(2)

(cos x + cos y ) ^(2) + (sin x - sin y ) ^(2) = 4 cos ^(2) ""(x + y )/( 2)

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

Prove that cos 2x cos "" x/2 -cos 3x cos " (9x)/(2) = sin 5x sin ""(5x)/(2).