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Question

Mathematics Question on limits of trigonometric functions

The value of lim⁡x→0cos⁡ xπ−x \displaystyle\lim_{x \to 0} \frac{\cos \, x}{\pi - x} is

A

π\pi

B

−π- \pi

C

1π \frac{1}{\pi}

D

−1π- \frac{1}{\pi}

Answer

1π \frac{1}{\pi}

Explanation

Solution

lim⁡x→0cos⁡ xπ−x=1π−0=1π \displaystyle\lim_{x \to 0} \frac{\cos \, x}{\pi - x} = \frac{1}{\pi - 0} = \frac{1}{\pi}