If A = sin2θ + cos4θ for any value of θ, then the value of A is?

Answer: Option B

$$\begin{array}{rl}& \text{According to the question, }\\ & \text{A}={\sin }^2\theta +\text{co}{\text{s}}^4\theta \\ & \text{Put }\theta =90^{\circ }\text{ for maximum value of A}\\ & \text{A}={\sin }^{2}90^{\circ }+\text{co}{\text{s}}^{4}90^{\circ }\\ & \text{A}=1+0\\ & \text{A}=1\\ & \text{Put }\theta =45^{\circ }\text{ for minimum value of A}\\ & \text{A}={\sin }^{2}45^{\circ }+\text{co}{\text{s}}^{4}45^{\circ }\\ & \text{A}=\frac{1}{2}+\frac{1}{4}\\ & \text{A}=\frac{3}{4}\\ & \therefore \text{A lies in }\frac{3}{4}⩽\text{A}⩽\text{1}\end{array}$$