Limit

Calculus Level 4

limx0(1xsinx1tan2x)=ab \displaystyle\lim_{x \rightarrow 0} \left( \dfrac{1}{x\sin x} - \dfrac{1}{\tan^2 x}\right) = \dfrac{a}{b}

Given that aa and bb are positive integers where gcd(a,b)=1\gcd (a,b)=1, find the value of a+ba+b.


Inspiration

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