Given x+1/x=2cosy then find x^n +1/x^n, Mathematics

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Here we know x can only be 1 or -1. so if it is 1 ans is 2.

if x is -1, for n even ans will be 2

if x is -1 and n is odd ans will ne -2.

so we can see evenfor negative x also ans is 2 while sgn you were using would give ans -2 so you can see 2 sgn(x) is wrong.

so ans will be 2 ecxept when x is -1 and n is odd then it will be -2.

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