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AP EAMCET202120 Aug 2021Morning ShiftMathematicsIndefinite IntegrationActual

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

Options

  1. Ax cot ( x )
  2. Bx tan ( x )
  3. Cx cos ( x )
  4. D1

Correct answer

A. x cot ( x )

Step-by-step solution

∫ cos ( x ) · d d x ( cosec ( x ) ) d x = ∫ cos ( x ) · - c o t x ( cosec ( x ) ) d x = - ∫ cos 2 x sin 2 x d x = - ∫ c o t 2 x d x = - ∫ ( cos e c 2 x - 1 ) d x = - ∫ cos e c 2 x d x - ∫ d x = c o t x + x + c f ( x ) . g ( x ) = x c o t x

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