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Class-11-science»Maths

$\lim_{x \to a} {\{\frac{\sin x}{\sin a}\}}^{\frac{1}{x - a}}$

\lim_{x \to a} {\{\frac{\sin x}{\sin a}\}}^{\frac{1}{(x - a)}} = \lim_{x \to a} {\{1 + \frac{\sin x}{\sin a} - 1\}}^{\frac{1}{(x - a)}} = \lim_{x \to a} {\{1 + \frac{\sin x - \sin a}{\sin a}\}}^{\frac{1}{(x - a)}} = e^{\lim_{x \to a} (\frac{\sin x - \sin a}{\sin a}) \times \frac{1}{(x - a)}} = e^{\lim_{x \to a} (\frac{2 \cos (\frac{x + a}{2}) \sin (\frac{x - a}{2})}{\sin a \times (\frac{x - a}{2}) \times 2})} = e^{\frac{\cos a}{\sin a}} = e^{\cot a}

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