Income tax on already taxed income

Sorry if my question is naive.  When we claim LTA without submitting any supporting documents the entire amount is taxable.  After paying tax (in the respective slab) for the claim if we invest the same in something like shares/mutual funds/fixed deposits less than 5 year etc. The profits gained (short term capital gain/interest/dividend etc) is again taxable.  Is there any rule to avoid such double taxing.  Is it possible to object such a double taxing.  Pl. clarify