Question

If $\cos A+{\cos }^{2}A=1,$ then the value of ${\sin }^{2}A+{\sin }^{4}A$ is equal to

Answer 1

${\sin }^{2}A+{\sin }^{4}A=1-{\cos }^{2}A+(1-{\cos }^{2}A{)}^2$
$=\cos A+{\cos }^{2}A,$ as given $\cos A+{\cos }^{2}A=1$
$=1$