Is The Set {cos1,cos2,cos3,cos4,...} under usual topology closed??? whatbiis its closure????

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1. What Is The closure of the set {cos1,cos2,cos3,cos4,...} under usual topology????
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2. If S=1/2^2cos1 + 1/cos1¤cos2+1/2^3 cos1 ¤cos2¤cos2^2 + .......... upto 10 terms . If S= sina(cotb-cotc) where a,b,c€N Then
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3. Given: f(closure(A)) subset of closure(f(A))Prove: For any closed set A in Y, f^-1(A) is closed in X (AKA f is continuous) X and
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4. y = 2[cos1/2(f1 - f2)x][cos1/2(f1 + f2)x]let f1 = 16 let f2 = 12 therefore y = 2[cos1/2(16 - 12)x][cos1/2(16 + 12)x] y =
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