If angles A , B and C are in A.P., then a + c b is equal to - Vidyadip

MCQ

If angles $A , B$ and C are in A.P., then $\frac{ a + c }{ b }$ is equal to

A
$2 \sin \frac{A- C }{2}$
✓
$2 \cos \frac{A- C }{2}$
C
$\cos \frac{ A - C }{2}$
D
$\sin \frac{A-C}{2}$

✓

Answer

Correct option: B.

$2 \cos \frac{A- C }{2}$

(B) $\frac{a+c}{b}=\frac{\sin A+\sin C}{\sin B}$
$=\frac{2 \sin \left(\frac{A+ C }{2}\right) \cos \left(\frac{ A - C }{2}\right)}{\sin B }$
$=\frac{2 \sin B}{\sin B } \cos \left(\frac{ A - C }{2}\right) \quad \ldots[\because 2 B= A + C ]$
$=2 \cos \left(\frac{A- C }{2}\right)$

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