展開する (cot(x)+1)(sqrt(3)cot(x)+1=0)

解

展開する

(cot (x) + 1) (3 cot (x) + 1 = 0)

3 cot^{2} (x) + cot (x) = 0

解答ステップ

(cot (x) + 1) (3 cot (x) + 1 = 0)

= (cot (x) + 1) (3 cot (x) + 1 \cdot 0 =)

FOIL メソッドを適用する:

(a + b) (c + d) = a c + a d + b c + b d

a = cot (x), b = 1, c = 3 cot (x), d = 1 = 0

cot (x) 3 cot (x) + cot (x) \cdot 1 = 0 + 1 \cdot 3 cot (x) + 1 \cdot 1 = 0

3 cot (x) cot (x) + 1 \cdot cot (x) = 0 + 1 \cdot 3 cot (x) + 1 \cdot 1 = 0

拡張

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

3 cot^{2} (x) + cot (x) = 0