cos4x=1-2 sin^2 2x

Question

Greetings all,

does anyone know any type of way to get cos4x=1-2 sin^2 2x started. Thanks

Answer 1

My English is not good, so I just write formula. I hope you can understand

Do you know Formula Trigonometry?

cos2x= 1-2sin^2x

then, we have: <=> cos4x= 1-2sin^2 (2x)

Answer 2

We can use the addition formula to get the double angle formula for cosine.

cos(2x)=cos(x+x)=cox(x)·cos(x)-sin(x)·sin(x)=cos²(x)-sin(x)² *

From a trig identy, cos²(x)=1-sin²(x), The equation above can be restated as follows:

cos(2x)=(1-sin²(x))-sin²(x)=1-2sin²(x)   We have: cos(2x)=1-2sin²(x) (=2cos²(x)-1)

This is the double angle formula.   By replacing x with 2x, we have:

cos(4x)=1-2sin²(2x)

* If we try the addition formula in a form like cos(4x)=cos(2x+2x), by using a trig identy, cos²(2x)=1-sin²(2x). we will directly get the equation/double angle formula: cos(4x)=1-2sin²(2x) (=2cos²(2x)-1).