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

The solution to 1/(1+cos(x))+1/(1-cos(x)) is 2csc^2(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 csc^{2} (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 ) + 1 ) ( - cos ( x ) + 1 )}

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

Simplify

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

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

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= 2 csc^{2} (x)

(3 x - 4) (3 x + 4)

2 x - 2 x

e^{x} + e^{x}

\frac{12}{100}

- 4 x^{5} (11 x^{3} + 2 x^{2} + 9 x + 1)

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