展開する sin^2(x)(cot(x)+1)^2

解

展開する

sin^{2} (x) (cot (x) + 1)^{2}

sin^{2} (x) csc^{2} (x) + 2 sin^{2} (x) cot (x)

解答ステップ

sin^{2} (x) (cot (x) + 1)^{2}

拡張

(cot (x) + 1)^{2} : cot^{2} (x) + 2 cot (x) + 1

= sin^{2} (x) (cot^{2} (x) + 2 cot (x) + 1)

分配法則を適用する:

m (a + b + c) = ma + mb + m c

sin^{2} (x) (cot^{2} (x) + 2 cot (x) + 1) = sin^{2} (x) cot^{2} (x) + sin^{2} (x) \cdot 2 cot (x) + sin^{2} (x) \cdot 1

= sin^{2} (x) cot^{2} (x) + sin^{2} (x) \cdot 2 cot (x) + sin^{2} (x) \cdot 1

簡素化

sin^{2} (x) cot^{2} (x) + sin^{2} (x) \cdot 2 cot (x) + sin^{2} (x) \cdot 1 : sin^{2} (x) (csc^{2} (x) + 2 cot (x))

= sin^{2} (x) (csc^{2} (x) + 2 cot (x))

分配法則を適用する:

a (b + c) = ab + a c

sin^{2} (x) (csc^{2} (x) + 2 cot (x)) = sin^{2} (x) csc^{2} (x) + sin^{2} (x) \cdot 2 cot (x)

= sin^{2} (x) csc^{2} (x) + sin^{2} (x) \cdot 2 cot (x)

= sin^{2} (x) csc^{2} (x) + 2 sin^{2} (x) cot (x)