展開する (1+tan(x))^3sec^2(x)

解

展開する

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

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

解答ステップ

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

= sec^{2} (x) (1 + tan (x))^{3}

拡張

(1 + tan (x))^{3} : 1 + 3 tan (x) + 3 tan^{2} (x) + tan^{3} (x)

= sec^{2} (x) (1 + 3 tan (x) + 3 tan^{2} (x) + tan^{3} (x))

括弧を分配する

= sec^{2} (x) \cdot 1 + sec^{2} (x) \cdot 3 tan (x) + sec^{2} (x) \cdot 3 tan^{2} (x) + sec^{2} (x) tan^{3} (x)

簡素化

sec^{2} (x) \cdot 1 + sec^{2} (x) \cdot 3 tan (x) + sec^{2} (x) \cdot 3 tan^{2} (x) + sec^{2} (x) tan^{3} (x) : sec^{2} (x) + 3 sec^{2} (x) tan (x) + 3 sec^{2} (x) tan^{2} (x) + sec^{2} (x) tan^{3} (x)

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