Question

In $\Delta$ $ABC$, lf $a,b,c$ are in $A.P$. then the value of $\frac{2Sin\frac{A}{2}Sin\frac{C}{2}}{Sin\frac{B}{2}}=$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (A)

$1$

It is given that a, b, c are in AP

Thus, $2b=a+c$

$2\frac{\sqrt{\frac{(s-b)(s-c)}{bc}}.\sqrt{\frac{(s-a)(s-b)}{ab}}}{\sqrt{\frac{(s-a)(s-c)}{ac}}}$

$=\frac{2(s-c)}{b}$

$=\frac{a+c-b}{b}$

$=\frac{a+c}{b}-1$

$=2-1$

$=1$