I wish to evaluate the following limit
$\lim_{x \to 0} [\ln (1+(\sin x)^2)][\cot(\ln (1+x)^2)]$
Can I distribute the limit over multiplication? And evaluate the limits of both the square brackets separately? If I am wrong how can this limit be found?
Edit : So can I rewrite it like this $\lim_{x \to 0} (\frac{ln(1+(\sin x)^2}{ (\sin x)^2})(\frac{ (\sin x)^2}{x^2})( {\ln (1+x)}^2\cot({\ln (1+x)}^2))(\frac{x^2}{ {\ln (1+x)}^2}) $
And then apply the standard limits to get the answer 1