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JEE Math Practice Question

$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\left[ {1 - \tan \left( {{x \over 2}} \right)} \right]\left[ {1 - \sin x} \right]} \over {\left[ {1 + \tan \left( {{x \over 2}} \right)} \right]{{\left[ {\pi - 2x} \right]}^3}}}$$ is

  1. A.$$\infty $$
  2. B.$${1 \over 8}$$
  3. C.0
  4. D.$${1 \over 32}$$

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