If cos θ + sec θ = $$\sqrt{3}$$​, then the value of cos³θ + sec³θ is:

Correct option is D

Cosθ + secθ = √3
Now cubing both sides we get,
Cos³​θ+sec³​θ+3cosθ.secθ (cosθ +secθ) = 3$$\sqrt{3}$$​
or, Cos³​θ+sec³​θ + 3$$\times1\times\sqrt{3}$$​=3$$\sqrt{3}$$​ 
or, Cos³​θ+sec^3​​θ = $$3 \sqrt{3}- 3\sqrt{3}$$  = 0