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JEE Main 7-April-2025 Paper - Shift 2 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 7-April-2025 Paper - Shift 24 Marks
Question
If the function $f(x)=\frac{\tan (\tan x)-\sin (\sin x)}{\tan x-\sin x}$ is continuous at $\mathrm{x}=0$, then $f(0)$ is equal to __________ .
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Answer

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

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