簡約 1/((1+sin(x)))+1/((1-sin(x)))

解

簡約

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

2 sec^{2} (x)

解答ステップ

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

結合

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

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

簡素化

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

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

基本的な三角関数の公式を使用する:

\frac{1}{cos ( x )} = sec (x)

= 2 sec^{2} (x)