Question

Упростить: 1 + cos8x

Answer 1

$cos2a=cos^2a-sin^2a=cos^2a-(1-cos^2a)=2cos^2a-1\; \Rightarrow \\\\cos2a=2cos^2a-1\; \; \Rightarrow \\\\\boxed {1+cos2a=2cos^2a}\; \; \Rightarrow \; \; 1+cos8x=2cos^24x$

$P.S.\; \; \; \; \; \boxed {1-cos2a=2sin^2a}$