Question

If in a $\Delta ABC$ $COSC=\frac{\sin A}{2\sin B}$ then $\Delta ABC$ is

• A. $equilateral$
• B. $isosceles$
• C. $rightangled$
• D. $obtuseangled$

Answer 1

The correct option is B $isosceles$

$\cos C=\frac{\sin A}{2\sin B}$

$\sin A=2\sin B\cos C$

$\sin A=\sin (B+C)+\sin (B-C)$

$\sin A=\sin ({180}^o-A)+\sin (B-C)$

$\sin A=\sin A+\sin (B-C)$

$\sin (B-C)$=0$

$B=C$

Triangle is isosceles $B$ is correct