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

A. $$\frac{1}{{\sqrt 2 }}$$

B. 1

C. 0

D. $$\sqrt 2 $$

Answer: Option C

Solution(By Examveda Team)

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