Question 927954
{{{2sin^2(x)-1=sin^4(x)-cos^4(x)}}}


start with right side

{{{sin^4(x)-cos^4(x)}}}

={{{(sin^2(x)-cos^2(x))(sin^2(x)+cos^2(x))}}}


={{{(sin^2(x)-(1-sin^2(x)))(sin^2(x)+(1-sin^2(x)))}}}


={{{(sin^2(x)-1+sin^2(x))*(cross(sin^2(x))+1-cross(sin^2(x))))}}}


={{{(2sin^2(x)-1)(1)}}}


={{{2sin^2(x)-1}}} which is our left side