Question

The value of $\underset{x\to a}{lim}\frac{\cos x-\cos a}{\cot x-\cot a}$, is;

• A. $-{\sin }^{3}a$
• B. ${\cos }^{3}a$
• C. ${\sin }^{3}a$
• D. $\cot a$

Answer 1

The correct option is C ${\sin }^{3}a$

$\underset{x\to a}{lim}\frac{\cos x-\cos a}{\cot x-\cot a}$ $\frac{0}{0}$ form

Using L'Hospital's rule we get,

$=\underset{x\to a}{lim}\frac{-\sin x}{-{\text{cosec}}^{2}x}$

$={\sin }^{3}a$.