Question

Найдите 16(sin^3x+cos^3x), если sinx+cosx=0,5

Answer 1

16(sin³x+cos³x)=16•(sinx+cosx)•(sin²x-sinxcosx+cos²x)=
=16•0.5•(1- sinxcosx)=8•(1- sinxcosx)=(sinx+cosx)²=sin²x+2sinxcosx+cos²x=1+2sinxcosx=0.5²  =>  sinxcosx=(0.25-1)/2=-0.375

8•(1+0.375)=11.

Answer 2

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