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If in ` A B C` , side `a , b , c` are in A.P. then `B > 60^0` (b) `B<60^0` `Blt=60^0` (d) `B=|A-C|`

A

`B gt 60^(@)`

B

`B lt 60^(@)`

C

`B le 60^(@)`

D

`B = |A - C|`

Text Solution

Verified by Experts

The correct Answer is:
C
`2b = a + c rArr 2 sin B = sin A + sin C`
or `4 sin.(B)/(2) cos.(B)/(2) = 2 sin ((A +C)/(2)) cos ((A -C)/(2))`
`rArr sin ((B)/(2)) = (1)/(2) cos (A - C) le (1)/(2) rArr B le 60^(@)`
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