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

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

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

simplify

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

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

Solution steps

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

Join

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

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

Simplify

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

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

\frac{72}{3}

- \frac{5}{4} + \frac{75}{40} + 1

4.25

1 - \frac{5}{12}

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