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 (x) tan (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 )}{( sin ( x ) + 1 ) ( - sin ( x ) + 1 )}

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

簡素化

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

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

簡素化

\frac{2 sin ( x )}{cos ^{2} ( x )} : 2 sec (x) tan (x)

= - 2 sec (x) tan (x)