Sides of `DeltaABC` are in A.P. If `a lt "min" {b,c}`, then cos A may be equal to

Options

A. `(4c - 3b)/(2b)`
B. `(4c - 3b)/(2c)`
C. `(3c - 4b)/(2c)`
D. `(4b - 3c)/(2b)`

Answer

B, D

Explanation

Sides are in `A.P.` and be `a lt min{b, c}`
`:.` order of `A.P.` can be `b, c, a` or `c, b, a`
if `2c = a + b` then `cos A = (b^(2) + c^(2) - a^(2))/(2bc)`
`= (b^(2) + c^(2) - (2c - b)^(2))/(2bc) = (4b - 3c)/(2b)`
if `2b = a + c`
then `cos A = (.b^(2) + c^(2) - (2b-c)^(2))/(2bc) = (4c - 3b)/(2c)`