Question

Prove the following statements :
${\cos }^{4}A-{\sin }^{4}A+1=2{\cos }^{2}A$.

Answer 1

$co{s}^{4}A-si{n}^{4}A+1$$=({\sin }^{2}A+{\cos }^{2}A)({\cos }^{2}A-{\sin }^{2}A)+1={\cos }^{2}A-{\sin }^{2}A+1={\cos }^{2}A+{\cos }^{2}A=2{\cos }^{2}A$