Differential of integration

Question:

!!int_(sinx)^1(t^2.f(t))dt!! !!=!! !!(1-sinx)!! for !!x!! !!∈!! !!(0,pi/2)!!
Then !!f(1/sqrt(3))!! !!=!! !!?!!
a)!!3!!
b)!!sqrt(3)!!
c)!!1/3!!
d)!!"None"!!

Solution-1:
If we try to compare the LHS and RHS of the above equation, we see that if the function
!!(t^2.f(t))!! !!=!! !!1!! , then it becomes; !!int_(sinx)^1(1.dt)!! !!=!! !!(1-sinx)!!

And that is equal to R.H.S.
So, we can say that here,
!!f(t)!! !!=!! !!1/(t^2)!!

Therefore
!!f(1/sqrt(3))!! !!=!! !!3!!

Solution-2:
Upon differentiating the function,we get
!!(1.f(1).0 + sin^2(x).f(sinx).cosx)!! !!=!! !!(-cosx)!!

That is,
!!f(sinx)!! !!=!! !!1/sin^2(x)!! Or !!f(p)!! !!=!! !!1/p^2!! where !!p!! !!=!! !!sin^2(x)!! for !!x!! !!∈!! !!(0,pi/2)!!

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