Question

In ΔABC, if `cosA/a = cosB/b,` then triangle ABC is ______ 

Options

• right-angled

• equilateral

• isosceles

• scalene

Answer 1

In ΔABC, if `cosA/a = cosB/b,` then triangle ABC is isosceles.

Explanation:

By sine rule,

`a/sinA = b/sinB = k`

⇒ a = k sin A, b = k sin B

Now, `cosA/a = cosB/b`

⇒ `cosA/(k sinA) = cosB/(k sinB)`

⇒ `cosA/sinA = cosB/sinB`

⇒ sin A cos B - cos A sin B = 0

⇒ sin (A - B) = 0

⇒ A - B = 0

⇒ A = B

ΔABC is an isosceles triangle.