If the function f(x) = tan(tan x) - sin(sin x)/tan x - sin x is continuous at x = 0, then f(0) is equal to _____.

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 _____.

Answer 1

Answer is: 2 

\(\lim\limits _{x \rightarrow 0} \frac{\frac{\tan (\tan x)-\tan x}{\tan ^{3} x} \frac{\tan ^{3} x}{x^{3}}+\frac{\tan x-\sin x}{x^{3}}+\frac{\sin x-\sin (\sin x)}{\sin ^{3} x} \frac{\sin ^{3} x}{x^{3}}}{\frac{\tan x-\sin x}{x^{3}}}\)   

\( =\frac{\frac{1}{3}+\frac{1}{2}+\frac{1}{6}}{\frac{1}{2}}=2\)