Question

With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.

पर्याय

• an isosceles triangle

• an equilateral triangle

• a right angled triangle

• a scalene triangle

Answer 1

With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is an isosceles triangle.

Explanation:

Using sine rule

`a/sinA = b/sinB` = K

We have, `cosA/a = cosB/b`

`\implies cosA/(K sin A) = cosB/(K sin B)`

`\implies` K sinB cosA = K sinA cosB

`\implies` cos A sin B – cos B sin A = 0

`\implies` sin (A – B) = 0

A = B

∴ Triangle in an isosceles triangle.