Question:
If $\cos A+\cos ^{2} A=1$ then $\left(\sin ^{2} A+\sin ^{4} A\right)=?$
(a) $\frac{1}{2}$
(b) 2
(c) 1
(d) 4
Solution:
Given : $\cos A+\cos ^{2} A=1$
$\cos A+\cos ^{2} A=1$
$\Rightarrow \cos A=1-\cos ^{2} A$
$\Rightarrow \cos A=\sin ^{2} A \quad\left(\because \sin ^{2} A+\cos ^{2} A=1\right)$
Now,
$\sin ^{2} A+\sin ^{4} A=\sin ^{2} A+\left(\sin ^{2} A\right)^{2}$
$=\cos A+(\cos A)^{2}$
$=\cos A+\cos ^{2} A$
$=1$
Hence, the correct option is (c).
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