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Find the range of f(x)=1/(2cosx-1)...

Find the range of `f(x)=1/(2cosx-1)`

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`-1 le cosx le 1`
or ` -2 le 2 cosx le 2`
or ` -3 le 2cos x -1 le 1`
For `(1)/(2cosx-1),`
`-3 le 2 cosx -1 lt 0 " or " 0 lt 2 cosx -1 le1`
i.e., `-oo lt (1)/(2cosx-1) le (-1)/(3) " or " 1 le (1)/(2cosx-1) lt oo`
Hence, the range is `(-oo,-(1)/(3)] cup [1, oo).`
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