Question 400530
{{{(sinx)^4-(cosx)^4=2(sinx)^2-1}}}
Lets work with left side 
{{{(sinx)^4-(cosx)^4}}}
Use FORMULA{{{a^2-b^2=(a-b)*(a+b)}}}
{{{(sinx)^4-(cosx)^4=((sinx)^2)^2-((cosx)^2)^2=((sinx)^2-(cosx)^2)*((sinx)^2+(cosx)^2)}}}
Use FORMULAS {{{(sinx)^2+(cosx)^2=1}}}
_____________{{{(cosx)^2=1-(sinx)^2}}}
{{{((sinx)^2-(cosx)^2)*((sinx)^2+(cosx)^2)=((sinx)^2-(1-(sinx)^2))*1=(sinx)^2-1+(sinx)^2=2(sinx)^2-1}}}
SO
{{{2(sinx)^2-1=2(sinx)^2-1}}} is an identity