What is (sin(x))/(1+sin(x))-(sin(x))/(1-sin(x)) ?

The solution to (sin(x))/(1+sin(x))-(sin(x))/(1-sin(x)) is -2tan^2(x)

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simplify (sin(x))/(1+sin(x))-(sin(x))/(1-sin(x))

simplify

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

- 2 tan^{2} (x)

Solution steps

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

Join

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

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

Simplify

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

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

Simplify

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

= - 2 tan^{2} (x)

(x - 2 y + z) (x + 2 y + z)

\frac{2 x - 6}{x ^{2} - 9} - \frac{x}{x + 3}

(2 m^{4})^{3}

\frac{sec ^{2} ( θ )}{csc ^{2} ( θ )}

\frac{20 - 26}{\frac{10}{80}}

What is (sin(x))/(1+sin(x))-(sin(x))/(1-sin(x)) ?
The solution to (sin(x))/(1+sin(x))-(sin(x))/(1-sin(x)) is -2tan^2(x)