展開する (1-tan^2(x))(1-tan^2(2x))tan(4x)

解

展開する

(1 - tan^{2} (x)) (1 - tan^{2} (2 x)) tan (4 x)

tan (4 x) - tan^{2} (2 x) tan (4 x) - tan^{2} (x) tan (4 x) + tan^{2} (x) tan^{2} (2 x) tan (4 x)

解答ステップ

(1 - tan^{2} (x)) (1 - tan^{2} (2 x)) tan (4 x)

= tan (4 x) (1 - tan^{2} (x)) (1 - tan^{2} (2 x))

FOIL方法

(1 - tan^{2} (x)) (1 - tan^{2} (2 x))

を適用します:

1 - tan^{2} (2 x) - tan^{2} (x) + tan^{2} (x) tan^{2} (2 x)

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

括弧を分配する

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

簡素化

tan (4 x) \cdot 1 + tan (4 x) (- tan^{2} (2 x)) + tan (4 x) (- tan^{2} (x)) + tan (4 x) tan^{2} (x) tan^{2} (2 x) : tan (4 x) - tan^{2} (2 x) tan (4 x) - tan^{2} (x) tan (4 x) + tan^{2} (x) tan^{2} (2 x) tan (4 x)

= tan (4 x) - tan^{2} (2 x) tan (4 x) - tan^{2} (x) tan (4 x) + tan^{2} (x) tan^{2} (2 x) tan (4 x)