Trigonometric Identity in My Book: Understanding (cos4x)^2 = 1+cos8x

[kasse]

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

 

[cristo]

Try looking at the identity for cos(2x)

 

[arunbg]

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

 

[kasse]

Try looking at the identity for cos(2x)

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

 

[cristo]

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.

 

[JJ420]

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

 

[kasse]

Yes, my mistake.

 

[cristo]

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

 

[kasse]

...

 

[dextercioby]

Nope.

$$\sin^{2} x=\frac{1-\cos 2x}{2}$$

Daniel.