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If sinθ+cosθ=p and sin3θ+cos3θ=q, then p(p2−3)=

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a

q

b

2q

c

-q

d

-2q

answer is D.

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Detailed Solution

cosθ+sinθ=p⇒p2=1+2sinθcosθ⇒sinθcosθ=p2−12 alsop3=cos3θ+sin3θ+3cosθsinθ(cosθ+sinθ)⇒p3=q+3p2−12p⇒2p3=2q+3p3−3p⇒p3−3p=−2q

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