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If \(\sin ^{2} \theta+\sin \theta=1\), then find \(\cos ^{4} \theta+\cos ^{2} \theta\)


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If \(\sin ^{2} \theta+\sin \theta=1\), then find \(\cos ^{4} \theta+\cos ^{2} \theta\)
in Mathematics by ♦ Diamond (71,587 points) | 64 views

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We have that \(\sin ^{2} \theta+\sin \theta=1\). Subtracting \(\sin ^{2} \theta\) from both sides and rearranging gives \(\sin \theta=1-\sin ^{2} \theta=\cos ^{2} \theta\). Then \(\cos ^{4} \theta+\cos ^{2} \theta=\cos ^{2} \theta\left(\cos ^{2} \theta+1\right)=\sin \theta(\sin \theta+1)=\sin ^{2} \theta+\sin \theta=1\).

 

Final Answer: The final answer is 1 .
by ♦ Diamond (71,587 points)

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