What is 1/(1-cos(θ))+1/(1+cos(θ)) ?

The solution to 1/(1-cos(θ))+1/(1+cos(θ)) is 2csc^2(θ)

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simplify 1/(1-cos(θ))+1/(1+cos(θ))

simplify

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

2 csc^{2} (θ)

Solution steps

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

Join

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

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

Simplify

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

= \frac{2}{sin ^{2} ( θ )}

Use the basic trigonometric identity:

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

= 2 csc^{2} (θ)

4 x^{4} - 8 x^{3} + 12 x^{2}

32 x^{2}

\frac{40}{52}

(x - 2) (2 x^{2} - 5 x - 9)

\frac{14}{100}

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