radomes.openskiesproject.org
Davad Davad
  • 20-07-2016
  • Mathematics
Answered

Rewrite sin3x with only sin x and cos x.

A2sin(x)cos^2(x) + cos(x)
B2sin(x)cos^2(x) + sin^3(x)
Csin(x)cos^2(x) - sin^3(x) + cos^3(x)
D2cos^2(x)sin(x) + sin(x) - 2sin^3(x)

Verified Answer :

dalendrk
dalendrk dalendrk
  • 24-07-2016

\(\sin3x=\sin(2x+x)=\sin2x\cos x+\sin x\cos2x\\\\=2\sin x\cos x\cos x+\sin x(\cos^2x-\sin^2x)\\\\=2\sin x\cos^2x+\sin x\cos^2x-\sin^3x\\\\=\boxed{3\sin x\cos^2x-\sin^3x}\)

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