Question Number 138735 by SanyamJoshi last updated on 17/Apr/21
Answered by Ajaypareek last updated on 17/Apr/21
$$\mathrm{1} \\ $$
Answered by bramlexs22 last updated on 18/Apr/21
$${let}\:\mathrm{sin}^{−\mathrm{1}} \left({x}\right)={t}\:\Rightarrow{x}=\mathrm{sin}\:{t} \\ $$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{t}.\mathrm{sin}\:\left(\mathrm{sin}\:{t}\right)}{\mathrm{sin}\:^{\mathrm{2}} {t}}\:= \\ $$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{t}}{\mathrm{sin}\:{t}}\:.\:\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{sin}\:{t}\right)}{\mathrm{sin}\:{t}}\:=\:\mathrm{1}×\mathrm{1}=\mathrm{1} \\ $$