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  4. (b-c/b+ c) cot (A/2)+(b+ c/b-c) tan (A/2)=

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Q. $\frac{b-c}{b+ c} \cot \frac{A}{2}+\frac{b+ c}{b-c} \tan \frac{A}{2}=$

Trigonometric Functions

Solution:

$\frac{b-c}{b +c} \cot \frac{A}{2}+\frac{b +c}{b-c} \tan \frac{A}{2}$
$=\tan \frac{B=C}{2}+\cot \frac{B-C}{2}$
$=\frac{2}{2 \sin \frac{B-C}{2} \cos \frac{B-C}{2}}=2 \text{cosec}(B-C)$