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If $sinθ + cosθ = p, \sin^{3} θ + \cos^{3} = q$ then $p (p^{2} - 3) =$

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-q

-2q

answer is D.

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Detailed Solution

$sinθ + cosθ = p, \sin^{3} θ + \cos^{3} θ = q \sin^{3} θ + \cos^{3} θ = (sinθ + cosθ) (\sin^{2} θ - sinθ cosθ + \cos^{2} θ) q = p (1 - \frac{p^{2} - 1}{2}) q = p \frac{(3 - p^{2})}{2} p (3 - p^{2}) = 2 q$

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