If `costheta+sectheta =sqrt(3)`, then the value of `(cos^(3)theta+sec^(3)theta)` is

Options

A. `(1)/(sqrt(2))`
B. 1
C. 0
D. `sqrt(2)`

Answer

c

Explanation

`cos theta+sec theta=sqrt(3)`
cubing both sides
`cos^(3)theta+sec^(3)theta+3cos thetasec theta`
`(cos theta+sec theta)=3sqrt(3)`
`cos^(3)theta+sec^(3)theta+3sqrt(3)=3sqrt(3)`
`cos^(3)theta+sec^(3)theta=0`