If $ \sin \mathrm{A}+\sin ^{2} \mathrm{~A}=1 $, then the value of the expression $ \left(\cos ^{2} \mathrm{~A}+\cos ^{4} \mathrm{~A}\right) $ is
(A) 1
(B) $ \frac{1}{2} $
(C) 2
(D) 3
Given:
\( \sin \mathrm{A}+\sin ^{2} \mathrm{~A}=1 \)
To do:
We have to find the value of the expression \( \left(\cos ^{2} \mathrm{~A}+\cos ^{4} \mathrm{~A}\right) \).
Solution:
We know that,
$\sin ^{2} A+\cos ^{2} A=1$
Therefore,
$\sin A+\sin ^{2} A =1$
$\sin A =1-\sin ^{2} A$
$=\cos ^{2} A$
Squaring on both sides, we get,
$\sin ^{2} A=\cos ^{4} A$
$1-\cos ^{2} A =\cos ^{4} A$
$\cos ^{2} A+\cos ^{4} A=1$
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