Question

Найдите 16(sin^3x+cos^3x)    если sinx+cosx=0.5

Answer 1

$sin^3+cos^3x=(sinx+cosx)(sin^2x-sinx*cosx+cos^2x)\ sin^2x+cos^2x=1\ tak kak \ (sinx+cosx)^2=0.5^2\ sinxcosx=-0.375\ sin^3x+cos^3x=0.5(1+0.375)=0.6875\ 16*0,6875=11$

Answer 2

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.