Question:
If cosA + cos2 A = 1, then sin2 A + sin4 A = 1
Solution:
True
$\because \quad \cos A+\cos ^{2} A=1$
$\Rightarrow \quad \cos A=1-\cos ^{2} A=\sin ^{2} A \quad\left[\because \sin ^{2} A+\cos ^{2} A=1\right]$
$\Rightarrow \quad \cos ^{2} A=\sin ^{4} A$
$\Rightarrow \quad 1-\sin ^{2} A=\sin ^{4} A$
$\Rightarrow \quad \sin ^{2} A+\sin ^{4} A=1$ $\left[\because \cos ^{2} A=1-\sin ^{2} A\right]$
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