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Exercise

lim⁡x→π3(csc⁡(x)1−tan⁡(x))\lim_{x\to\frac{\pi}{3}}\left(\frac{\csc\left(x\right)}{1-\tan\left(x\right)}\right)

Step-by-step Solution

1

Evaluate the limit lim⁡x→π3(csc⁡(x)1−tan⁡(x))\lim_{x\to{\frac{\pi }{3}}}\left(\frac{\csc\left(x\right)}{1-\tan\left(x\right)}\right) by replacing all occurrences of xx by π3\frac{\pi }{3}

csc⁡(π3)1−tan⁡(π3)\frac{\csc\left(\frac{\pi }{3}\right)}{1-\tan\left(\frac{\pi }{3}\right)}

Final answer to the exercise

csc⁡(π3)1−tan⁡(π3)\frac{\csc\left(\frac{\pi }{3}\right)}{1-\tan\left(\frac{\pi }{3}\right)}

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limx→π3 (csc(x)1−tan(x) )
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