Algebra and Trigonometry 10th Edition

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