Question

simplify the expression by using a double angle formula

cos^2 4theta-sin^2 4theta

Answer 1

Double angle formula for cos(2x) is
cos(2x)=cos^2(x)-sin^2(x)

Substitute x=4theta, then
cos(8theta)=cos^2(4theta)-sin^2(4theta)
=>
cos^2(4theta)-sin^2(4theta) = cos(8theta)