# Trigonometric identity

In my book, (cos4x)^2 is written 1+cos8x without refering to any formula. Which trig. identity is used here?

cristo
Staff Emeritus
Try looking at the identity for cos(2x)

The correct identity is (cos4x)^2 = (1+cos8x)/2 .

Try looking at the identity for cos(2x)

You mean cos(2x) = (cosx)^2 - (sinx)^2 ?

cristo
Staff Emeritus
You mean cos(2x) = (cosx)^2 - (sinx)^2 ?

Yes, and as arunbg says, there is a factor of 1/2 missing from your given identity.

the identity is cos^2x = (1 + cos2x)/2 is it not?

Yes, my mistake.

cristo
Staff Emeritus
the identity is cos^2x = (1 + cos2x)/2 is it not?

One can derive this from the double angle identity for cos(2x) using further the identity that cos2x+sin2x=1

..........

Last edited:
dextercioby
$$\sin^{2} x=\frac{1-\cos 2x}{2}$$