Question

If $\cos \theta +\sec \theta =\sqrt{3}$ then the value of ${\cos }^3\theta +{\sec }^3\theta =$

• A. $3\sqrt{3}$
• B. $2\sqrt{3}$
• C. $0$
• D. $1$

Answer 1

Answer: (C)

$0$

Given,

$\cos \theta +\sec \theta =\sqrt{3}$......(1).

Now cubing both sides we get,

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

or, ${\cos }^3\theta +{\sec }^3\theta +3\sqrt{3}=3\sqrt{3}$ [ Using (1)]

or, ${\cos }^3\theta +{\sec }^3\theta =0$.