What is the limit as x approaches pi of (x-pi)csc(x) ?

The limit as x approaches pi of (x-pi)csc(x) is -1

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limit as x approaches pi of (x-pi)csc(x)

x \to π lim ((x - π) csc (x))

- 1

Solution steps

x \to π lim ((x - π) csc (x))

Rewrite for L'Hopital

= x \to π lim (\frac{x - π}{\frac{1}{c s c ( x )}})

Apply L'Hopital's Rule

= x \to π lim (\frac{1}{cos ( x )})

Plug in the value

x = π

= \frac{1}{cos ( π )}

Simplify

\frac{1}{cos ( π )} : - 1

= - 1

What is the limit as x approaches pi of (x-pi)csc(x) ?
The limit as x approaches pi of (x-pi)csc(x) is -1