展開する (1+tan(x))(1-tan(x))sec^2(x)

解

展開する

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

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

解答ステップ

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

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

2つの正方形の差

(1 + tan (x)) (1 - tan (x)) を適用します : 1 - tan^{2} (x)

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

分配法則を適用する:

a (b - c) = ab - a c

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

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

規則を適用する:

a \cdot 1 = a

sec^{2} (x) \cdot 1 = sec^{2} (x)

= sec^{2} (x) - sec^{2} (x) tan^{2} (x)