Biến đổi biểu thức thành nhân tử: 2sinxcosx – 2sin ²x + 3sinx – cosx – 1 03/12/2021 Bởi Madeline Biến đổi biểu thức thành nhân tử: 2sinxcosx – 2sin ²x + 3sinx – cosx – 1
Ta có $2\sin x \cos x – 2\sin^2x + 3\sin x – \cos x – 1 = 2\sin x(\cos x – \sin x) + \sin x – \cos x + 2\sin x – 1$ $= 2\sin x(\cos x – \sin x) – (\cos x – \sin x) + 2\sin x – 1$ $= (2\sin x – 1)(\cos x- \sin x) + 2\sin x – 1$ $= (2\sin x – 1)(\cos x – \sin x + 1)$ Vậy $2\sin x \cos x – 2\sin^2x + 3\sin x – \cos x – 1 =(2\sin x – 1)(\cos x – \sin x + 1)$ Bình luận
Ta có
$2\sin x \cos x – 2\sin^2x + 3\sin x – \cos x – 1 = 2\sin x(\cos x – \sin x) + \sin x – \cos x + 2\sin x – 1$
$= 2\sin x(\cos x – \sin x) – (\cos x – \sin x) + 2\sin x – 1$
$= (2\sin x – 1)(\cos x- \sin x) + 2\sin x – 1$
$= (2\sin x – 1)(\cos x – \sin x + 1)$
Vậy
$2\sin x \cos x – 2\sin^2x + 3\sin x – \cos x – 1 =(2\sin x – 1)(\cos x – \sin x + 1)$