If \(\cos (x)+\cos ^2(x)=1\), then \(\sin ^2(x)+\sin ^4(x)\) is equal to
If \(\cos (x)+\cos ^2(x)=1\), then \(\sin ^2(x)+\sin ^4(x)\) is equal to
0
1
-1
2
Solution
It is given that,
\(\begin{aligned}
\cos x+\cos ^2 x & =1 \Rightarrow \cos x=\sin ^2 x \\
\therefore \quad \sin ^2 x+\sin ^4 x & =\cos x+\cos ^2 x=1
\end{aligned}\)
Hence, option (b) is correct.