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).