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

The solution to 1/(1+cos(x))-1/(1-cos(x)) is -2cot(x)csc(x)

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

simplify

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

- 2 cot (x) csc (x)

Solution steps

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

Join

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

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

Simplify

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

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

Simplify

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

= - 2 cot (x) csc (x)

(x + 8)^{3}

\frac{1}{2} \times (- 2)

\frac{56}{3}

(12 a^{5} - 6 a - 10 a^{3}) - (10 a - 2 a^{5} - 14 a^{4})

(6 x + 9 y) 2

What is 1/(1+cos(x))-1/(1-cos(x)) ?
The solution to 1/(1+cos(x))-1/(1-cos(x)) is -2cot(x)csc(x)