Question

In $△ABC$, If $a\cos A=b\cos B$, then the triangle is

• A. Isosceles
• B. Right angled
• C. Isosceles or right angled
• D. Right angled isosceles

Answer 1

The correct option is C Isosceles or right angled

According to sine Rule

$\frac{a}{\sin A}=\frac{b}{\sin B}$ ...(1)

If $a\cos A=b\cos B$

Then $\frac{a}{\cos B}=\frac{b}{\cos A}$

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

From eq. (1)

$b=\frac{\sin B}{\sin A}a$

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

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

$\sin 2A=\sin 2B$

Many $A=B$ or $A=90-B$

Triangle is isoceles or right angled