簡約 ((cot(A)+csc(A))(cot(A)-csc(A)))/((1-cos(A))(1+cos(A)))

解

簡約

\frac{( cot ( A ) + csc ( A ) ) ( cot ( A ) - csc ( A ) )}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

- csc^{2} (A)

解答ステップ

\frac{( cot ( A ) + csc ( A ) ) ( cot ( A ) - csc ( A ) )}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

簡素化

(cot (A) + csc (A)) (cot (A) - csc (A)) : - 1

= \frac{- 1}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

分数の規則を適用する:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

(1 + cos (A)) (1 - cos (A)) = sin^{2} (A)

= - \frac{1}{sin ^{2} ( A )}

簡素化

\frac{1}{sin ^{2} ( A )} : csc^{2} (A)

= - csc^{2} (A)