sin^4A-cos^4A=1-2cos^2A

\sin^4{A}-\cos^4{A}=(\sin^2{A}-\cos^2{A})(\sin^2{A}+\cos^2{A}) $$\\ \\ $$ \sin^2{A}+\cos^2{A}=1 $$\\ $$ \sin^2{A}-\cos^2{A}=1-\cos^2{A}-\cos^2{A}=1-2\cos^2{A} $$\\ \\ So, using the last two lines in the first line we have:\\ $$ \sin^4{A}-\cos^4{A}=1-2\cos^2{A}$$