If ∫ cos ( x ) · d d x ( cosec ( x ) ) d x = f ( x ) + g ( x ) + c , then f ( x ) · g ( x ) =

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

  1. xcot(x)
  2. xtan(x)
  3. xcos(x)
  4. 1

Solution

∫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

 

Asked in: AP EAMCET 2021 (20 Aug Shift 1)

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