The greatest value of sin4θ + cos4θ is?

Answer: Option D

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