If cosθ + secθ = 3 , then the value of (cos3θ + sec3θ) is?

Answer: Option C

$$\begin{array}{rl}& \text{cos}\theta +\sec \theta =\sqrt{3}\\ & \text{Cubing both sides}\\ & \text{co}{\text{s}}^3\theta +{\sec }^3\theta +3\text{cos}\theta \sec \theta \left(\text{cos}\theta +\sec \theta \right)=3\sqrt{3}\\ & \text{co}{\text{s}}^3\theta +{\sec }^3\theta +3\sqrt{3}=3\sqrt{3}\\ & \text{co}{\text{s}}^3\theta +{\sec }^3\theta =0\end{array}$$