Is there an easy mwt od to find solution to the following Relation and function question?

Is there an easy mwt od to find solution to the following Relation and function question? 12. Let sc (O, 71) denotes set of values of x. If 81+1coo (c) (b) (d) a' 43, then S = 27t 27t 3

Dear Student,
Please find below the solution to the asked query:

We havex0,π, hence cosx-1,1cosx[0,1)Now81+cosx+cos2x+cos3x+....=4381+cosx+cos2x+cos3x+....=223 =26....iAs X2=X2Now 1+cosx+cos2x+cos3x+.... is a geometric progression G.P.of infinite terms, with common ratio=cosx1 =cosxand as cosx[0,1) and hence formula for sum of  infinite terms of G.P. can be applied1+cosx+cos2x+cos3x+....=First Term1-common ratio=11-cosxHence i becomes811-cosx =262311-cosx=26311-cosx=611-cosx=21-cosx=12cosx=12cosx=12 or cosx=-12Hence x=π3 or x=2π3

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I mean "easy method"
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