Question

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

Answer 1

$\sin A+{\sin }^{2}A=2\Rightarrow {\sin }^{2}A+\sin A-2=0\Rightarrow (\sin A+2)(\sin A-1)=0\Rightarrow \sin A=1(\because \sin A\in [-1,1\left]\right)\Rightarrow \cos A=\sqrt{1-{\sin }^{2}A}=0$

Therefore,
$\cos A+{\cos }^{2}A+{\cos }^{4}A=0$