If cosθ + secθ = √3 , then the value of

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If cosθ + secθ = √3 , then the value of (cos³θ + sec³θ) is :

1. 1
2. 1
  √2
3. 0
4. √2

Correct Option: C

a³ + b³ = (a + b)³ - 3ab(a + b)
∴ cos³θ + sec³θ = (cosθ + secθ)³ - 3cosθ . secθ(cosθ + secθ)
cos³θ + sec³θ = ( √3 )³ - 3 × √3
{ ∵ cosθ + secθ = √3 }
cos³θ + sec³θ = 3√3 - 3√3 = 0