展開する (1-cos(x))(cot(x)+csc(x)=sin(x))

解

展開する

(1 - cos (x)) (cot (x) + csc (x) = sin (x))

cot (x) + csc (x) = sin (x)

解答ステップ

(1 - cos (x)) (cot (x) + csc (x) = sin (x))

= (1 - cos (x)) (cot (x) + = csc (x) sin (x))

FOIL メソッドを適用する:

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

a = 1, b = - cos (x), c = cot (x), d = csc (x) = sin (x)

1 \cdot cot (x) + 1 \cdot csc (x) = sin (x) + (- cos (x)) cot (x) + (- cos (x)) csc (x) = sin (x)

マイナス・プラスの規則を適用する

+ (- a) = - a

1 \cdot cot (x) + 1 \cdot csc (x) = sin (x) - cos (x) cot (x) - cos (x) csc (x) = sin (x)

拡張

1 \cdot cot (x) + 1 \cdot csc (x) : cot (x) + csc (x)

cot (x) + csc (x) = sin (x)