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AP EAMCET201922 Apr 2019Morning ShiftMathematicsDifferentiationActual

If (f(t)= 1+ cosec t 1- cosec t ) for (0 < t < 2 ) and (f^ (t)=f(t) g(t) ), then (g(t)= )

Options

  1. A(-4 cosec 2 t )
  2. B(4 cosec 2 t )
  3. C(2 2 t )
  4. D(4 cosec t )

Correct answer

B. (4 cosec 2 t )

Step-by-step solution

Given, (f(t)= 1+ cosec t 1- cosec t ) Differentiating w.r.t. (t ), we get ((1- cosec t)(- cosec t t) ) ( aligned f^ (t) & = -(1- cosec t)( cosec t t) (1- cosec t)^2 & = - cosec t t+ cosec ^2 t t (1- cosec t)^2 & = -2 cosec t t (1- cosec t)^2 1+ cosec t 1+ cosec t & = ( 1+ cosec t 1- cosec t ) (- 2 cosec t t 1- cosec ^2 t ) & =f(t) 2 cosec t t ^2 t =f(t) 2 cosec ^2 t ^2 t & =f(t) 2 t t =f(t)(4 cosec 2 t)=f(t) g(t) [given] aligned ) So, (g(t)=4 cosec 2 t )

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