In `DeltaABC` if `a cos B =b cosA` then which of the following is always correct :

Options

A. `DeltaABC` is an equilateral traingle
B. `DeltaABC` is an isosceles traingle
C. `DeltaABC` is an isosceles right angle traingle
D. None of these

Answer

D

Explanation

`z^(2)+az+b=0`
`& |z_(1)+z_(2)|=|z_(1)|+|z_(2)|`
`implies" "z_(2)=kz_(1)(kgt0)`
Now
`z_(1)+z_(2)=-a" "z_(1)z_(2)=b`
`impliesz_(1)(k+1)=-a" "implies" "kz_(1)^(2)=b`
Given `a^(2)=lambda b`
`implies (k+1)^(2)=lambda k`
`implies lambda=((k+1)^(2))/(k)=k+(1)/(2)+2`
Minimum value of `lambda` is 4