In `DeltaABC, bc=2b^(2)cos A+2c^(2)cos A-4bc cos^(2)A`, then `Delta ABC` is

Options

A. isosceles but not necessarily equilateral
B. equilateral
C. right angled but not necessarily isosceles
D. right angled isosceles

Answer

A

Explanation

`bc=2b^(2)cos A+2c^(2)cos A-4bc cos^(2)A`
`rArr bc=2 cos A(b^(2)+c^(2)-2bc cos A)`
`rArr bc=(2 cos A)a^(2)`
`rArr (bc)/(2a^(2))=cos A=(b^(2)+c^(2)-a^(2))/(2bc)`
`rArr b^(2)c^(2)=a^(2)(b^(2)+c^(2)-a^(2))`
`rArr (a^(2)-b^(2))(a^(2)-c^(2))=0`
Thus, triangle is isosceles.