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Let g (x) be a differentiable function ...

Let g (x) be a differentiable function satisfying `(d)/(dx){g(x)}=g(x) and g (0)=1` , then `g(x)((2-sin2x)/(1-cos2x))dx` is equal to

A

`g(x)cotx+C`

B

`-g(x)cotx+C`

C

`(g(x))/(1-cos2x)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
We have , `(d)/(dx){g(x)}=g(x)`
`rArrg'(x)=g(x)`
`rArrint(g(x))/(g(x))dx=int1 . dx`
`rArr log_(e){g(x)}=x+logCrArrg(x)=Ce^(x)`
Now , g`(0)=1rArrc=1`
`rArr g (x)=e^(x)`
`rArrintg(x)(2-sinx)/(1-cosx)dx`
`=inte^(x)("cosec"^(2)x-cotx)dx=-e^(x)cot+C=-g(x)cotx+C`
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