Question

If in a triangle $ABC,\sin A\cos B=1/4$ and $3\tan A=\tan B$, then the triangle is

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

Answer 1

The correct option is A right angled

$\frac{\tan A}{\tan B}=\frac{1}{3}\Rightarrow \frac{\sin A\cos B}{\cos A\sin B}=\frac{1}{3}$
Put $\sin A\cos B=\frac{1}{4}\therefore \cos A\sin B=\frac{3}{4}$
$\therefore \sin (A+B)=\frac{1}{4}+\frac{3}{4}=1or\sin C=1=\sin \frac{\pi }{2}\therefore C=\frac{\pi }{2}$
Hence triangle is right angled.