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This question already has an answer here:

Is it possible to find the following limit without applying L'Hopital's Rule, but only with some transformations? $$\lim_{x\to0}\frac{1-cos(x)}{x^2}$$

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marked as duplicate by lab bhattacharjee limits Jun 28 '17 at 8:26

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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Hint: write $$\frac{(1-\cos(x))(1+\cos(x))}{x^2(1+\cos(x))}$$

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