证明下列不等式:-|||-(1)当 lt (x)_(1)lt (x)_(2)lt dfrac (pi )(2) 时, dfrac (tan {x)_(2)}(tan {x)_(1)}gt dfrac ({x)_(2)}({x)_(1)};-|||-(2)当 gt 0 时, ln (1+x)gt dfrac (arctan x)(1+x);-|||-(3)当 lt alt blt (e)^2 时, (ln )^2b-(ln )^2agt dfrac (4)({e)^2}(b-a).