You need more parentheses.
√((1 - cosx)/(1 + cosx)) =
√((1 - cosx)/(1 - cosx) (1 - cosx)/(1 + cosx)) =
√((1 - cosx)^2/(1 - cos^2x)) =
√((1 - cosx)^2/sin^2x) =
(1 - cosx)/|sinx|
Square root always yields a non-negative number. The range of sinx is [-1, 1] so you need the absolute value of sinx in the denominator. 1 - cosx ≥ 0 for all x so absolute value is not needed for the numerator.
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You need more parentheses.
√((1 - cosx)/(1 + cosx)) =
√((1 - cosx)/(1 - cosx) (1 - cosx)/(1 + cosx)) =
√((1 - cosx)^2/(1 - cos^2x)) =
√((1 - cosx)^2/sin^2x) =
(1 - cosx)/|sinx|
Square root always yields a non-negative number. The range of sinx is [-1, 1] so you need the absolute value of sinx in the denominator. 1 - cosx ≥ 0 for all x so absolute value is not needed for the numerator.