Question

If a, b, c the sides of ΔABC are in A.P. and a is the smallest side then cosA equals

(a) [(3c – 4b)/2c]

(b) [(3c – 4b)/2b]

(c) [(4c – 3b)/2c]

(d) of these

Answer 1

The correct option (c) [(4c – 3b)/2c]

Explanation:

we know, cosA = [(b2 + c2 – a2)/(2bc)]

∵ a, b, c are in A.P

∴ 2b = a + c

∴ cosA = [{b2 + c2 – (2b – c)2}/(2bc)]

∴ cosA = [{b2 + c2 – (4b2 + c2 – 4bc)}/(2bc)]

= [(– 3b2 + 4bc)/(2bc)]

= [(– 3b + 4c)/2c]

= [(4c – 3b)/2c].