A) \[\frac{1}{2}{{\sin }^{3}}a\]
B) \[\frac{1}{2}\text{cose}{{\text{c}}^{2}}a\]
C) \[{{\sin }^{3}}a\]
D) \[\text{cose}{{\text{c}}^{3}}a\]
Correct Answer: C
Solution :
\[\underset{x\to a}{\mathop{\lim }}\,\,\frac{\cos x-\cos a}{\cot x-\cot a}=\underset{x\to a}{\mathop{\lim }}\,\,\left( \frac{-\sin x}{-\cos e{{c}^{2}}x} \right)=\underset{x\to a}{\mathop{\lim }}\,{{\sin }^{3}}x={{\sin }^{3}}a\].
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