Answer
Identity is verified.
$sin^4x+cos^4x=1-2~cos^2x+2~cos^4x$
Work Step by Step
We know that:
$sin^2x+cos^2x=1$
$sin^2x=1-cos^2x$
Start at the left side of the equation:
$sin^4x+cos^4x=(sin^2x)^2+cos^4x=(1-cos^2x)^2+cos^4x=1-2~cos^2x+(cos^2x)^2+cos^4x=1-2~cos^2x+cos^4x+cos^4x=1-2~cos^2x+2~cos^4x$
