Question Number 131181 by john_santu last updated on 02/Feb/21
![lim_(x→0) ((1/x) − tan ((π/2)−x))=?](https://www.tinkutara.com/question/Q131181.png)
$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{x}}\:−\:\mathrm{tan}\:\left(\frac{\pi}{\mathrm{2}}−{x}\right)\right)=? \\ $$
Answered by Ar Brandon last updated on 02/Feb/21
![L=lim_(x→0) ((1/x) − tan ((π/2)−x))=lim_(x→0) ((1/x)−cotx) =lim_(x→0) {((1−xcotx)/x)}=lim_(x→0) {((1−cosx)/x)}=0](https://www.tinkutara.com/question/Q131182.png)
$$\mathscr{L}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{x}}\:−\:\mathrm{tan}\:\left(\frac{\pi}{\mathrm{2}}−{x}\right)\right)=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{x}}−\mathrm{cotx}\right) \\ $$$$\:\:\:\:=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\frac{\mathrm{1}−\mathrm{xcotx}}{\mathrm{x}}\right\}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\frac{\mathrm{1}−\mathrm{cosx}}{\mathrm{x}}\right\}=\mathrm{0} \\ $$
Answered by john_santu last updated on 02/Feb/21
![](https://www.tinkutara.com/question/18467.png)