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Calculus Level 2

lim ⁡ x → 0 cot ⁡ ( 2 x ) csc ⁡ ( x ) = ? \large \lim_{x \to 0} \frac {\cot (2x)}{\csc (x)} = \ ?


The answer is 0.5.

Abu Bakar Khan by Abu Bakar Khan , 31, India

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1 solution

lim ⁡ x → 0 cot ⁡ ( 2 x ) csc ⁡ ( x ) = lim ⁡ x → 0 cos ⁡ ( 2 x ) sin ⁡ ( 2 x ) 1 sin ⁡ x = lim ⁡ x → 0 cos ⁡ ( 2 x ) 2 sin ⁡ x cos ⁡ x × sin ⁡ x = lim ⁡ x → 0 cos ⁡ ( 2 x ) 2 cos ⁡ x = 1 2 = 0.5 \begin{aligned} \lim_{x \to 0} \frac {\cot (2x)}{\csc (x)} & = \lim_{x \to 0} \frac {\frac {\cos (2x)}{\sin (2x)}}{\frac 1{\sin x}} = \lim_{x \to 0} \frac {\cos (2x)}{2 \sin x \cos x} \times \sin x = \lim_{x \to 0} \frac {\cos (2x)}{2 \cos x} = \frac 12 = \boxed{0.5} \end{aligned}

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@Abu Bakar Khan , you can cut and paste or key in LaTex codes into the pages of Brilliant.org. I edited a few of your problems here.

Chew-Seong Cheong - 4 years, 9 months ago

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Oh thank you!!

Abu Bakar Khan - 4 years, 9 months ago

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