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Question Number 92239 by jagoll last updated on 05/May/20

$$\underset{x\to 0}{\lim }\frac{1-\mid \cos 7\mathrm{x}\mid }{1-\mid \tan 5\mathrm{x}\mid }=$$

Commented by john santu last updated on 05/May/20

$$\underset{x\to 0}{\lim }\frac{1-{\cos }^{2}7\mathrm{x}}{1-\tan {}^{2}5\mathrm{x}}\times \frac{1+\mid \tan 5\mathrm{x}\mid }{1+\mid \cos 7\mathrm{x}\mid }$$$$\underset{x\to 0}{\lim }\frac{\sin {}^{2}7\mathrm{x}}{2-\sec {}^{2}5\mathrm{x}}\times \frac{1}{2}=0$$

Commented by john santu last updated on 05/May/20

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Commented by Prithwish Sen 1 last updated on 05/May/20

$$\mathrm{sir}\mathrm{how}1-{\tan }^{2}5\mathrm{x}={\sec }^{2}5\mathrm{x}?$$

Commented by john santu last updated on 05/May/20

$$\mathrm{haha}..\mathrm{typo}$$

Commented by Prithwish Sen 1 last updated on 05/May/20

$$\because \mathrm{x}\to 0\Rightarrow \mid \mathrm{tanx}\mid \to 0\mathrm{and}\mid \mathrm{cosx}\mid \to 1$$$$\therefore \mathrm{l}\underset{\mathrm{x}\to 0}{\mathrm{im}}\frac{1-\mid \mathrm{cosx}\mid }{1-\mid \mathrm{tanx}\mid }=\frac{1-1}{1-0}=0$$

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