Given that `cos(x/2).cos(x/4).cos(x/8)..... = sinx/x` Prove that `(1/2^2)sec^2(x/2) +(1/2^4)sec^2(x/4) +..... = cosec^2x - 1/(x^2)`

Given that cosx/2.cosx/4.cosx/8....=sinx/x Then find the sum 1/2^2sec^2x/2+1/2^4sec^2x/4+...

Prove that cos4x = 2cos^2(2x) - 1

Given that (cos x)/(2)*(cos x)/(4)*(cos x)/(8)...=(sin x)/(x) Then find the sum (1)/(2^(2))(sec^(2)x)/(2)+(1)/(2^(4))(sec^(2)x)/(4)+...

Prove that cos 4(x)=1-8 sin ^(2) (x) cos ^(2) (x)

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

Prove that : 2sec^(2)x-sec^(4)x-2cos ec^(2)x+cos ec^(4)x=(1-tan^(8)x)/(tan^(4)x)

Prove that: 1+cos2x+cos4x+cos6x=4cos x cos2x cos3x

Prove that (1)/(sec x-tan x)+(1)/(sec x+tan x)=(2)/(cos x)

Prove that (sec8x-1)/(sec4x-1)=(tan8x)/(tan2x)

If x=(11 pi)/4 , prove that : sin^2 x- cos^2 x+2 tan x- sec^2 x=1 .