Question

If the sides of a triangle are proportional to the cosines of the opposite angles then the triangle is

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

Answer 1

The correct option is B equilateral

Given, $\frac{\cos A}{\cos B}=\frac{a}{b}$

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

$\cos A\sin B=\sin A\cos B$

$\sin (A-B)=0$

$A=B$.

Similarly, $\frac{\cos B}{\cos C}=\frac{b}{c}$

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

$\sin (B-C)=0$

$B=C$

But , $A=B$

Hence, $A=B=C$

Hence equilateral triangle.