Question

Phân tích các biểu thức sau thành nhân tử

A = sinx + sin2x + sin 3x - cosx - cos2x - cos3x

Answer 1

\(A=\left(\sin x+\sin3x\right)+\sin2x-\left(\cos x+\cos3x\right)-\cos2x\)

\(=2\cdot\sin2x\cdot\cos x+\sin2x-2\cdot\cos2x\cdot\cos x-\cos2x\)

\(=\sin2x\left(2\cos x+1\right)-\cos2x\left(2\cos x+1\right)\)

\(=\left(2\cos x+1\right)\left(\sin2x-\cos2x\right)\)

Answer 2

A= (sin x + sin 3x) + sin 2x - (cos x + cos 3x) - cos 2x

= 2 ⋅ sin 2x ⋅ cos x + sin 2x - 2 ⋅ cos2x ⋅ cos x - cos 2x

= sin 2x (2 cos x + 1) - cos 2x (2 cos x + 1)

= (2 cos x + 1) (sin 2x - cos 2x)