Question

Show that ${\cos }^{4}A+{\sin }^{4}A+2{\sin }^{2}A{\cos }^{2}A=1$

Answer 1

$({\cos }^{2}A{)}^2+({\sin }^{2}A{)}^2+2{\sin }^{2}A{\cos }^{2}A$

$({\sin }^{2}A+{\cos }^{2}A{)}^2=(1{)}^2$

$[\because a^2+b^2+2ab=(a+b{)}^2]$