Question

In a triangle ABC, if cos A + 2cos B + cos C = 2, then a, b, c

are in –

• A. A. P.
• B. G. P.
• C. H. P.
• D. None of these

Answer 1

Answer: (A)

A. P.

Answer 2

cos A + 2cos B + cos C = 2

̃ cos A + cos C = 4 sin²

̃ 2cos $\left( \frac { \mathrm { A } + \mathrm { C } } { 2 } \right)$ cos = 4 sin² $\left( \frac { B } { 2 } \right)$

̃ cos = 2cos $\left( \frac { \mathrm { A } + \mathrm { C } } { 2 } \right)$

$\left[ \because \cos \left( \frac { \mathrm { A } + \mathrm { C } } { 2 } \right) = \sin \left( \frac { \mathrm { B } } { 2 } \right) \right]$

̃ cot A/2 cot C/2 = 3

$\sqrt { \frac { s ( s - a ) } { ( s - b ) ( s - c ) } }$ × $\sqrt { \frac { s ( s - c ) } { ( s - a ) ( s - b ) } }$ = 3

̃ s = 3(s – b) ̃ 2s = 3b ̃ a + c = 2b

̃ a, b, c are in A.P.