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)

- x^{2} - x

(4 a + 2) (6 a^{2} - a + 2)

2^{2 l o g_{2} (3) + 2 l o g_{2} (5)}

\frac{40}{9}

(b + 10)^{3}

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)