证明:(cosx+sinx)(cos2x+sin2x)
=cosxcos2x+cosxsin2x+sinxcos2x+sinxsin2x
=(cosxcos2x+sinxsin2x)+(cosxsin2x+sinxcos2x)
=(cosxcos2x+sinxsin2x)+sin3x
=[cosx(1-2sinx^2)+sinx 2sinxcosx]+sin3x
=[cosx(1-2sinx^2+2sinx^2)]+sin3x
=cosx+sin3x
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