If the function $f(x)=\frac{ an ( an x)-\sin (\sin x)}{ an x-\sin x}$ is continuous at $\mathrm{x}=0$, then $f(0)$ is equal to ________

Question

If the function $f(x)=\frac{	an (	an x)-\sin (\sin x)}{	an x-\sin x}$ is continuous at $\mathrm{x}=0$, then $f(0)$ is equal to ________

Aicharya · Accepted Answer

$\lim _{x ightarrow 0} \frac{\frac{	an (	an x)-	an x}{	an ^3 x} \frac{	an ^3 x}{x^3}+\frac{	an x-\sin x}{x^3}+\frac{\sin x-\sin (\sin x)}{\sin ^3 x} \frac{\sin ^3 x}{x^3}}{\frac{	an x-\sin x}{x^3}}$ $=\frac{\frac{1}{3}+\frac{1}{2}+\frac{1}{6}}{\frac{1}{2}}=2$

If the function $f(x)=\frac{\tan (\tan x)-\sin (\sin x)}{\tan x-\sin x}$ is continuous at $\mathrm{x}=0$,…

Solution