Question

If $2\sin C\cos A=\sin B$, then $\Delta ABC$ is

• A. Right angled triangle
• B. Isosceles triangle
• C. Equilateral triangle
• D. None of these

Answer 1

Answer: (B)

Isosceles triangle

In $\Delta ABC$, $2\sin C\cos A=\sin B$ [given]
$\Rightarrow \sin (C+A)+\sin (C-A)=\sin B$
$[\because 2\sin A\cos B=\sin (A+B)+\sin (A-B)]$
$\Rightarrow \sin ({180}^o-B)+\sin (C-A)=\sin B$
$[\because \angle A+\angle B+\angle C={180}^o]$
$\Rightarrow \sin B+\sin (C-A)=\sin B$
$\Rightarrow \sin (C-A)=0=\sin 0^o$
$\Rightarrow C-A=0$
$\Rightarrow C=A$
Hence, $\Delta ABC$ is an isosceles triangle.