Question

If in a ΔABC `a cos^2(C/2) + c cos^2(A/2) = (3b)/2`, then the sides a, b and c ______.

विकल्प

• satisfy a + b = c

• are in A.P

• are in G .P

• are in H.P

Answer 1

If in a ΔABC `a cos^2(C/2) + c cos^2(A/2) = (3b)/2`, then the sides a, b and c are in A.P.

Explanation:

Given that, `a cos^2(C/2) + c cos^2(A/2) = (3b)/2`

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

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

We know that, b = a cos C + c cos B

a + c + b = 3b or a + c = 2b or a, b, c are in A.P.