sin3theta+cos3 theta / sin theta+cos theta = 1-sin theta.cos theta

sin3θ + cos3θ​ / sinθ​ + cosθ​ 
= (sinθ + cosθ)(sin2θ + cos​2θ - sinθcosθ) / (sinθ + cosθ)
= (sinθ + cosθ)( 1 - sinθcosθ) / (sinθ + cosθ)
= 1 - sinθcosθ

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