Evaluate the following limit: _ x 2 2x - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\frac{\pi}{2}}}\frac{\sin2\text{x}}{\cos\text{x}}$

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Answer

$\lim\limits_{\text{x}\rightarrow{\frac{\pi}{2}}}\frac{\sin2\text{x}}{\cos\text{x}}$ $=\lim\limits_{\text{x}\rightarrow\frac{\pi}{2}}\frac{2\sin\text{x}\cos\text{x}}{\cos\text{x}}$ $=2\lim\limits_{\text{x}\rightarrow\frac{\pi}{2}}\sin\text{x}$ $=2\times\sin\frac{\pi}{2}$ $=2\times1$ $=2$

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