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The number of solution of equation 2cos^...

The number of solution of equation `2cos^(-1)x=a+a^2(cos^(-1)x)^(-1)` are at least (a) 1 if `a in [-2pi,pi]-{0}` (b) 1 if `a` ` in (0,pi]` (c) 1 if `a in [-2pi,0)` (d) `2` if `a >0`

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