簡約 (cos(x))/(sec(x)+1)+(cos(x))/(sec(x)-1)

解

簡約

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

2 cot^{2} (x)

解答ステップ

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

結合

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

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

簡素化

(sec (x) + 1) (sec (x) - 1) : tan^{2} (x)

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

基本的な三角関数の公式を使用する:

\frac{1}{tan ( x )} = cot (x)

= 2 cot^{2} (x)