The greatest value of $\sin ^{4} \theta+\cos ^{4} \theta$ is.

A. 2
B. 3
C. $\frac{1}{2}$
D. 1

Answer: Option D

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Solution(By Apex Team)

 

$\begin{array}{l}\sin^2\theta+\cos^2\theta=1\\
\text{Squaring both sides}\\
\begin{array}{l}
\sin ^{4} \theta+\cos ^{4} \theta \\
=1-2 \sin ^{2} \theta \cdot \cos ^{2} \theta \\
\operatorname{Put} \theta=90^{\circ} \\
=1-2 \sin ^{2} 90^{\circ} \times \cos ^{2} 90^{\circ} \\
=1-0 \\
=1
\end{array}\end{array}$