Question

If $a=4,b=5,c=7$, find the value of $\cos \frac{B}{2}$.

Answer 1

$a=4,b=5,c=7$ [ Given ]

We know,

$\Rightarrow$ $\cos B=\frac{a^2+c^2-b^2}{2ac}$

$\Rightarrow$ $\cos B=\frac{(4{)}^2+(7{)}^2-(5{)}^2}{4\times 7}$

$\Rightarrow$ $\cos B=\frac{16+49-25}{28}$

$\Rightarrow$ $\cos B=\frac{40}{28}$

$\Rightarrow$ $\cos B=\frac{10}{7}$

$\Rightarrow$ $\cos \frac{B}{2}=\sqrt{\frac{1+\cos B}{2}}$

$=\pm \sqrt{\frac{1+\frac{10}{7}}{2}}$

$=\pm \sqrt{\frac{17}{14}}$