Evaluate `lim_(xtooo) xlog_(e){(sin(a+(1)/(x)))/(sina)},0ltalt(pi)/(2).`

Explanation

To evaluate the limit

\[ \lim_{x \to \infty} x \log\left(\frac{\sin\left(a + \frac{1}{x}\right)}{\sin a}\right), \quad 0 < a < \frac{\pi}{2}, \]

we will follow these steps:

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