Question

If in a $\Delta ABC,2\cos A\sin C=\sin B$ then the triangle is

• A. equilateral
• B. isosceles
• C. right angled
• D. none of these

Answer 1

The correct option is B isosceles

Given, $2\cos A.\sin C=\sin B$

$2\cos A.\left(\frac{\sin C.c}{c}\right)=\frac{\sin B.b}{b}$

Now ,
$\frac{\sin C}{c}=\frac{\sin B}{b}$

Hence
$2\cos A.c=b$

$(b^2+c^2-a^2)=b^2$

$c^2=a^2$

$|c|=|a|$

Hence an isosceles triangle.