Cos^4(x)=1/4(1+2cos(2x)+cos^2(2x)

verify.

thanks

First factor the right side:

1/4(1+2cos(2x)+cos^2(2x)) = [1/2(1+cos(2x))]^2

Using the trig identity cos(2x) = 2cos^2(x)-1 the right side is

[1/2(1+2cos^2(x)-1)]^2 = [cos^2(x)]^2 = cos^4(x)

EDIT: In response to some of the posts below, you can't verify it by plugging in one number, otherwise I could "verify" that sin(x) = cos(x) by plugging in 45 degrees.

cos^4(x)=1/4(1+2cos(2x)+cos^2(2x)?
Shouldn't it be
cos^4(x)=(1/4)(1+2cos(2x)+cos^2(2x)? Check it please, will you?

Use any value of x and verify! What is the difficulty there?
Take x = 60 then LHS = 1/16, RHS = (1/4)(1-1+(1/4)) = 1/16. It simple.
When it comes to proving it, it is different,

put x=1
cos^4(x) =0.08522
(1/4)(1+2cos(2x)+cos^2(2x)) =0.08522
Hence verified.