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

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

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