Question

In ΔABC, with usual notations, if a, b, c are in A.P. Then `a cos^2 (C/2) + c cos^2(A/2)` = ______.

Options

• `3 a/2`

• `3 c/2`

• `3 b/2`

• `(3abc)/2`

Answer 1

In ΔABC, with usual notations, if a, b, c are in A.P. Then `a cos^2 (C/2) + c cos^2(A/2)` = `underlinebb(3 b/2)`.

Explanation:

∵ a, b, c are in A.P.

∴ 2b = a + c  ........(i)

Now, `a cos^2 (C/2) + c cos^2(A/2)` 

= `a([1 + cos C])/2 + c([1 + cos A])/2`

= `(a + c + a cos C + C cos A)/2`

= `(a + c + b)/2`  ...[∵ b = a cos C + c cos A]

= `(2b + b)/2`  ...[Using equation (i)]

= `(3b)/2`