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Please find below the solution to the asked query:

We haveL.H.S.=cosx+sin3π2+x-sin3π2-x+cosπ+xAs sin3π2+x=sin3π2-x=-cosx and cosπ+x=-cosx, hence we getL.H.S.=cosx-cosx--cosx-cosx=cosx-cosx+cosx-cosx=0 =R.H.S. Proved

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