Question

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

• A. $2\sin (B-C)$
• B. $2\mathrm{cosec}(B-C)$
• C. $2\tan (B-C)$
• D. $2\cot (B-C)$

Answer 1

Answer: (B)

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