展開する 2sec^2(x)tan^2(x)(tan(x)+sec(x))

解

展開する

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

2 sec^{2} (x) tan^{3} (x) + 2 sec^{3} (x) tan^{2} (x)

解答ステップ

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

分配法則を適用する:

a (b + c) = ab + a c

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

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

簡素化

2 sec^{2} (x) tan^{2} (x) tan (x) + 2 sec^{2} (x) tan^{2} (x) sec (x) : 2 sec^{2} (x) tan^{3} (x) + 2 sec^{3} (x) tan^{2} (x)

= 2 sec^{2} (x) tan^{3} (x) + 2 sec^{3} (x) tan^{2} (x)