limx→0 cos⁡(sin⁡x)−1×2=

# $\underset{x\to 0}{lim} \frac{\mathrm{cos}\left(\mathrm{sin}x\right)-1}{{x}^{2}}=$

1. A

1

2. B

$-1$

3. C

$1/2$

4. D

$-1/2$

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### Solution:

We have,

$\begin{array}{l}\underset{x\to 0}{lim} \frac{\mathrm{cos}\left(\mathrm{sin}x\right)-1}{{x}^{2}}\\ =-\underset{x\to 0}{lim} \frac{1-\mathrm{cos}\left(\mathrm{sin}x\right)}{{\mathrm{sin}}^{2}x}×\frac{{\mathrm{sin}}^{2}x}{{x}^{2}}\end{array}$

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