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\begin{array} { l } { \text { EXAMPLE } 3 \text { Prove that: } } \\ { \text { (i) } \tan ^ { - 1 } \left\{ \frac { \sqrt { 1 + \cos x } + \sqrt { 1 - \cos x } } { \sqrt { 1 + \cos x } - \sqrt { 1 - \cos x } } \right\} = \frac { \pi } { 4 } + \frac { x } { 2 } , 0 < x < \frac { \pi } { 2 } } \end{array}

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