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If int(sinx)^(1)t^(2)f(t)dt=1-sinx, xeps...

If `int_(sinx)^(1)t^(2)f(t)dt=1-sinx, xepsilon(0,(pi)/2)` then find the value of `f(1/(sqrt(3)))`

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We have `int_(sinx)^(1)t^(2)f(t)dt=1-sinx`
Differentiating both side w.r.t `x`, we get
`1^(2)xxf(1)xx0-sin^(2)x xx f(sinx)xxcosx=-cosx`
`impliesf(sinx)=1/(sin^(2)x)`
`:.f(1/(sqrt(3)))=3`.
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