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JEE Math Practice Question

A function $$y=f(x)$$ satisfies $$f(x) \sin 2 x+\sin x-\left(1+\cos ^2 x\right) f^{\prime}(x)=0$$ with condition $$f(0)=0$$. Then, $$f\left(\frac{\pi}{2}\right)$$ is equal to

  1. A.2
  2. B.1
  3. C.$$-$$1
  4. D.0

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