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(sin³ x + cos³ x) / (sin x + cos x)
= (sin x + cos x)(sin² x + cos² x - sin x cos x) / (sin x + cos x)
= (sin² x + cos² x - sin x cos x)
= 1 - 1/2 sin 2x
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*
(sin³ x + cos³ x) / (sin x + cos x)
= (sin x + cos x)(sin² x + cos² x - sin x cos x) / (sin x + cos x)
= (sin² x + cos² x - sin x cos x)
= 1 - 1/2 sin 2x