展開する (1-2sin^2(x)-cos^2(x))*cot^2(x)

解

展開する

(1 - 2 sin^{2} (x) - cos^{2} (x)) \cdot cot^{2} (x)

- cos^{2} (x)

解答ステップ

(1 - 2 sin^{2} (x) - cos^{2} (x)) cot^{2} (x)

= cot^{2} (x) (1 - 2 sin^{2} (x) - cos^{2} (x))

分配法則を適用する:

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

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

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

簡素化

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

= - cos^{2} (x)