SOLUTION: Prove that each is an identity (sin^3 x + cos^3 x)/ (sin x + cos x) = 1 - (sin 2 x/ 2)

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Question 443330: Prove that each is an identity
(sin^3 x + cos^3 x)/ (sin x + cos x) = 1 - (sin 2 x/ 2)
Answer by lwsshak3(11628) About Me  (Show Source):
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Prove that each is an identity
(sin^3 x + cos^3 x)/ (sin x + cos x) = 1 - (sin 2 x/ 2)
..
Start with left side
Use sum of cubes
[(sinx+cosx)(sin^2x-sinxcosx+cos^2x)]/(sin x + cos x)
cancel (sin x + cos x) and use identity sin^2+cos^2=1
=1-sinxcosx*(2/2)
=1-(2sinxcosx)/2=1-(sin 2x/2)
left side=right side