If $\mathrm{f}(x)=\left(\frac{1+ an x}{1+\sin x} ight)^{\operatorname{cosec} x}$ is continuous at $x=0$, then $f(0)$ is equal to

Question

If $\mathrm{f}(x)=\left(\frac{1+	an x}{1+\sin x}ight)^{\operatorname{cosec} x}$ is continuous at $x=0$, then $f(0)$ is equal to

Aicharya · Accepted Answer

$\begin{aligned} f(0) & =\lim _{x ightarrow 0} f(x) \ & =\lim _{x ightarrow 0}\left(\frac{1+	an x}{1+\sin x}ight)^{\operatorname{cosec} x} \ & =\left(\frac{1+0}{1+0}ight)^1 \ & =1\end{aligned}$

If $\mathrm{f}(x)=\left(\frac{1+\tan x}{1+\sin x}\right)^{\operatorname{cosec} x}$ is continuous at $x=0$,…

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