If $sin\theta+sin^{2}\theta=1$, then evaluate $cos^{2}\theta+cos^{4}\theta$.

Given: $sin\theta+sin^{2}\theta=1$.

To do: To evaluate $cos^{2}\theta+cos^{4}\theta$.

Solution: 

As given $sin\theta+sin^{2}\theta=1$

$\Rightarrow sin\theta+1-cos^{2}\theta=1$                     [$\because sin^{2}\theta+cos^{2}\theta=1$]

$\Rightarrow sin\theta-cos^{2}\theta=0$

$\Rightarrow sin\theta=cos^{2}\theta$

Now on substituting $sin\theta=cos^{2}\theta$ in $cos^{2}\theta+cos^{4}\theta$

$\Rightarrow cos^{2}\theta+cos^{4}\theta=sin\theta+sin^{2}\theta=1$       [Given $sin\theta+sin^{2}\theta=1$]

$\therefore cos^{2}\theta+cos^{4}\theta=1$

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Updated on: 10-Oct-2022

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