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AP EAMCET · Maths · Indefinite Integration

If cos(x)·ddx(cosec(x))dx=f(x)+g(x)+c, then f(x)·g(x)=

  1. A xcot(x)
  2. B xtan(x)
  3. C xcos(x)
  4. D 1
Verified Solution

Answer & Solution

Correct Answer

(A) xcot(x)

Step-by-step Solution

Detailed explanation

∫cos(x)·ddx(cosec(x))dx =∫cos(x)·-cotx(cosec(x))dx =-∫cos2xsin2xdx =-∫cot2xdx =-∫(cosec2x-1)dx =-∫cosec2xdx-∫dx =cotx+x+c f(x).g(x)=xcotx