hkrayon hkrayon
  • 02-08-2016
  • Mathematics
contestada

solve 3sinx-4sin^3 x= -1

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caylus
caylus caylus
  • 02-08-2016
Hello,

Since 3sin x-4sin^3x=sin (3x)  (*****)
3sin x-4sin^3x=-1
==>sin (3x)=-1
==>3x=3π/2 +2kπ
==>x=π/2+2kπ/3, k being an integer

(*****)
sin (3x)=sin(x+2x)=sin x cos2x+cos x sin 2x
=sin x(cos²x-sin²x)+2cos²x sin x
=sin x(cos²x+2cos²x-sin²x)
=sinx(3(1-sin²x)-sin²x)
=3sin x-4sin^3x
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