Question

If $\sin A+{\sin }^{2}A=1$ then show that ${\cos }^{4}A+{\cos }^{2}A=1$

Answer 1

Given,

$\sin A+{\sin }^{2}A=1$

or, $\sin A=1-{\sin }^{2}A$

or, $\sin A={\cos }^{2}A$......(1).

Now,

${\cos }^{4}A+{\cos }^{2}A$

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

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

$=1$.