展開する (sin(x)+1)(sin(x)-1)(4sin(x)+1)

解

展開する

(sin (x) + 1) (sin (x) - 1) (4 sin (x) + 1)

- 4 cos^{2} (x) sin (x) - cos^{2} (x)

解答ステップ

(sin (x) + 1) (sin (x) - 1) (4 sin (x) + 1)

拡張

(sin (x) + 1) (sin (x) - 1) (4 sin (x) + 1) : - cos^{2} (x) (4 sin (x) + 1)

= - cos^{2} (x) (4 sin (x) + 1)

分配法則を適用する:

a (b + c) = ab + a c

- cos^{2} (x) (4 sin (x) + 1) = - cos^{2} (x) \cdot 4 sin (x) - cos^{2} (x) \cdot 1

= - cos^{2} (x) \cdot 4 sin (x) - cos^{2} (x) \cdot 1

簡素化

- cos^{2} (x) \cdot 4 sin (x) - cos^{2} (x) \cdot 1 : - 4 cos^{2} (x) sin (x) - cos^{2} (x)

= - 4 cos^{2} (x) sin (x) - cos^{2} (x)