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

Question

If ∫ cos ( x ) · d d x ( cosec ( x ) ) d x = f ( x ) + g ( x ) + c , then f ( x ) · g ( x ) =, x cot ( x ), x tan ( x ), x cos ( x ), 1

MARKS App · Accepted Answer

∫ 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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