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Values of Trigonometric Ratios

Evaluate: li...

Question

Evaluate: $lim x \to 0 cos x cot 2 x$

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Solution

${lim}_{x \to 0} c o s x c o t 2 x$
= ${lim}_{x \to 0} \frac{c o s x . c o s 2 x}{s i n 2 x}$
= ${lim}_{x \to 0} \frac{c o s x . c o s 2 x}{2 s i n x c o s x}$
$= \frac{1}{2} {lim}_{x \to 0} \frac{c o s 2 x}{c o s x}$
$= \frac{1}{2} \frac{c o s 0}{c o s 0} = \frac{1}{2}$

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