簡約 1/(1+cos(x))+1/(1-cos(x))

解

簡約

\frac{1}{1 + cos ( x )} + \frac{1}{1 - cos ( x )}

2 csc^{2} (x)

解答ステップ

\frac{1}{1 + cos ( x )} + \frac{1}{1 - cos ( x )}

結合

\frac{1}{1 + cos ( x )} + \frac{1}{1 - cos ( x )} : \frac{2}{( cos ( x ) + 1 ) ( - cos ( x ) + 1 )}

= \frac{2}{( cos ( x ) + 1 ) ( - cos ( x ) + 1 )}

簡素化

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

= \frac{2}{sin ^{2} ( x )}

基本的な三角関数の公式を使用する:

\frac{1}{sin ( x )} = csc (x)

= 2 csc^{2} (x)