In a ` Delta A B C ,` if `cos A=( sin B)/(2sin C),` then show that `c=adot`

Explanation

Since `\cos A=\frac{\sin B}{2 \sin C}`,

we have `\frac{{b}^{2}+{c}^{2}-{a}^{2}}{2 {ab}}=\frac{{b}}{2 {c}}` or `b^{2}+c^{2}-a^{2}=b^{2}` or `c^{2}=a^{2}`. Hence `c=a`


So we can say `\triangle A B C` is isosceles.