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\(\lim\limits_{x\to \frac\pi4} \frac{2 - cosec^2x}{1 - cotx}\) |
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Answer» \(\lim\limits_{x\to \frac\pi4} \frac{2 - cosec^2x}{1 - cotx}\) \((\frac 00 - case)\) \(= \lim\limits_{x\to \frac\pi4} \frac{-2\,cosecx(-cosecx \;cotx)}{-(-cosec^2x)}\) (By D.L.H. Rule) \(=\lim\limits_{x\to \frac\pi4} \frac{2cosec^2x \,cotx}{cosec^2 x}\) \(= \lim\limits_{x\to \frac\pi4 } 2\,cot x \) \(= 2\,cot\frac\pi4\) \( = 2\) |
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