Question

Rewrite sin3x with only sin x and cos x.
A) 2sin(x)cos^2(x) + cos(x)
B) 2sin(x)cos^2(x) + sin^3(x)
C) sin(x)cos^2(x) - sin^3(x) + cos^3(x)
D) 2cos^2(x)sin(x) + sin(x) - 2sin^3(x)

Answer 1

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