展開する (sec(x)tan(x))(tan(x)-1)

解

展開する

(sec (x) tan (x)) (tan (x) - 1)

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

解答ステップ

(sec (x) tan (x)) (tan (x) - 1)

分配法則を適用する:

a (b - c) = ab - a c

(sec (x) tan (x)) (tan (x) - 1) = sec (x) tan (x) tan (x) - sec (x) tan (x) \cdot 1

= sec (x) tan (x) tan (x) - sec (x) tan (x) \cdot 1

簡素化

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

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