Question

Show that each statement is true: Cos^4X-sin^4X=2cos^2X-1

Answer 1

$cox^4x-sin^4x=2cos^2x-1\\\\ (cosx^2-sin^2x)(cosx^2x+sin^2x)=2cos^2x-1\\\\ cosx^2-sin^2x*1=2cos^2x-1\ \ \ | subtract\ 2cos^2x\\\\ -cosx^2-sin^2x=-1\ \ \ | multiply\ by\ -1\\\\ cosx^2+sin^2x=1\\\\ 1=1$