展開する tan^2(x)-sin^2(x)(cot^2(x)+tan(x))^2

解

展開する

tan^{2} (x) - sin^{2} (x) (cot^{2} (x) + tan (x))^{2}

tan^{2} (x) - sin^{2} (x) cot^{4} (x) - 2 sin^{2} (x) cot^{2} (x) tan (x) - sin^{2} (x) tan^{2} (x)

解答ステップ

tan^{2} (x) - sin^{2} (x) (cot^{2} (x) + tan (x))^{2}

拡張

(cot^{2} (x) + tan (x))^{2} : cot^{4} (x) + 2 cot^{2} (x) tan (x) + tan^{2} (x)

= tan^{2} (x) - sin^{2} (x) (cot^{4} (x) + 2 cot^{2} (x) tan (x) + tan^{2} (x))

分配法則を適用する:

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

- sin^{2} (x) (cot^{4} (x) + 2 cot^{2} (x) tan (x) + tan^{2} (x)) = - sin^{2} (x) cot^{4} (x) - sin^{2} (x) \cdot 2 cot^{2} (x) tan (x) - sin^{2} (x) tan^{2} (x)

= tan^{2} (x) - sin^{2} (x) cot^{4} (x) - sin^{2} (x) \cdot 2 cot^{2} (x) tan (x) - sin^{2} (x) tan^{2} (x)

= tan^{2} (x) - sin^{2} (x) cot^{4} (x) - 2 sin^{2} (x) cot^{2} (x) tan (x) - sin^{2} (x) tan^{2} (x)