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In any DeltaABC, prove that (i) tan""(...

In any `DeltaABC`, prove that
(i) `tan""(B-C)/2=(b-c)/(b+c)cot""A/2`.
(ii) If `angleB=90^(@)`, prove that `tan(A/2)=sqrt(((b-c)/(b+c)))`.
(iii) If `angleC=90^(@)`, prove that `tan((A−B)/2)/tan((A+B)/2)=(a-b)/(a+b)`.

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