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If angles A,B, and C are in A.P., then (...

If angles `A,B, and C` are in `A.P.,` then `(a+c)/b` is equal to

A

`2 "sin" (A-C)/2`

B

`2 "cos" (A-C)/2`

C

`"cos"(A-C)/2`

D

`"sin"(A-C)/2`

Text Solution

Verified by Experts

The correct Answer is:
B
`A+B+C=pi`
`2B=A+C`
`implies3B=piimpliesB=(pi)/3`
`:.(a+c)/b=(sin A+sin C)/(sinB)`
`=(2"sin"(A+C)/2 "cos"(A-C)/2)/("sin"(pi)/3)`
`=(2"sin"(pi)/3"cos"(A-C)/2)/("sin"(pi)/3)=2"cos"(A-C)/2`
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