QJEEM03Ma9537: JEE Main 2003 Mathematics - Class 11 JEEM03Ma9537 Solution: If in a Δ A B C a cos 2 ( C 2 ) + c cos 2 ( A 2 ) = 3 b 2 ,…

Question

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If in a

Δ A B C

a \cos^{2} (\frac{C}{2}) + c \cos^{2} (\frac{A}{2}) = \frac{3 b}{2},

then the sides

a, b

and

c

:

Accepted Answer

If

a \cos^{2} (\frac{C}{2}) + c \cos^{2} (\frac{A}{2}) = \frac{3 b}{2}

a [\cos C + 1] + c [\cos A + 1] = 3 b

(a + c) + (a \cos C + c \cos B) = 3 b

a + c + b = 3 b

or

a + c = 2 b

or

a, b, c

are in

A . P .

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