Sides of a triangle ABC are in A.P. If `a lt min{b,c}`,then cosA may be equal to

Options

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

Answer

A, D

Explanation

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