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Question Number 176154 by cortano1 last updated on 14/Sep/22

$$\underset{x\to 0}{\lim }\frac{\tan \mathrm{x}-\mathrm{x}}{\mathrm{x}-\sin \mathrm{x}}=?$$

Answered by adhigenz last updated on 14/Sep/22

$$=\underset{x\to 0}{\lim }\frac{{\sec }^{2}x-1}{1-\cos x}$$$$=\underset{x\to 0}{\lim }\frac{1-{\cos }^{2}x}{{\cos }^{2}x(1-\cos x)}$$$$=\underset{x\to 0}{\lim }\frac{(1-\cos x)(1+\cos x)}{{\cos }^{2}x(1-\cos x)}$$$$=\underset{x\to 0}{\lim }\frac{1+\cos x}{{\cos }^{2}x}$$$$=\frac{1+1}{1}$$$$=2$$

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