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

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

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

simplify

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

2 tan (x)

Solution steps

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

Join

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

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

Simplify

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

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

Rewrite using trig identities

= 2 tan (x)

(2 x + 5) (3 x - 1)

\frac{27}{90}

\frac{2}{5} \cdot \frac{3}{2}

sin (v) csc (v) - \frac{sin ( v )}{csc ( v )}

3 (- \frac{2}{3})

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