If $$\cos\theta + \sec\theta = \sqrt{3}$$, then the value of $$(\cos^{3}\theta + \sec^{3}\theta)$$ is:

Given : $$\cos\theta + \sec\theta = \sqrt{3}$$ ----------(i)

Cubing both sides, we get :

=> $$(\cos\theta + \sec\theta)^3 = (\sqrt{3})^3$$

=> $$cos^3\theta+sec^3\theta+3(cos\theta)(sec\theta)(cos\theta+sec\theta)=3\sqrt3$$

=> $$cos^3\theta+sec^3\theta+3(cos\theta\times sec\theta)(\sqrt3)=3\sqrt3$$

$$\because$$ $$cos\theta\times sec\theta=1$$ and using equation (i),

=> $$cos^3\theta+sec^3\theta=3\sqrt3-3\sqrt3=0$$

=> Ans - (C)