Question:
If $\cos A+\cos ^{2} A=1$, then $\sin ^{2} A+\sin ^{4} A=$
(a) −1
(b) 0
(c) 1
(d) None of these
Solution:
Given:
$\cos A+\cos ^{2} A=1$
$\Rightarrow 1-\cos ^{2} A=\cos A$
So,
$\sin ^{2} A+\sin ^{4} A$
$=\sin ^{2} A+\sin ^{2} A \sin ^{2} A$
$=\sin ^{2} A+\left(1-\cos ^{2} A\right)\left(1-\cos ^{2} A\right)$
$=\sin ^{2} A+\cos A \cos A$
$=\sin ^{2} A+\cos ^{2} A$
$=1$
Hence, the correct option is (c).