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Question

sin3x+cos3x=(sinx+cosx)(1sinxcosx)

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Solution

sin3x+cos3x=(sinx+cosx)(1sinxcosx)

sin3x+cos3xsinx+cosx=(1sinxcosx)

LHS

a3+b3=(a+b)(a22ab+b2)

sin3x+cos3xsinx+cosx=(sinx+cosx)(sin2xsinxcosx+cos2x)sinx+cosx

sin2xsinxcosx+cos2x

identity

sin2x+cos2x=1

sin2xsinxcosx+cos2x

1sinxcosx

hence,RHS is proved.

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