Question

In ΔABC, if `"a" cos^2  "C"/2 + "c" cos^2  "A"/2 = (3"b")/2`, then a, b, c are in ______.

Options

• A. P.

• G. P.

• H. P.

• none of these

Answer 1

In ΔABC, if `"a" cos^2  "C"/2 + "c" cos^2  "A"/2 = (3"b")/2`, then a, b, c are in A. P..

Explanation:

`"a" cos^2  "C"/2 + "c" cos^2  "A"/2 = (3"b")/2`

⇒ `"a"((1 + cos "C")/2) + "c"((1 + cos"A")/2) = (3"b")/2`

⇒ `("a" + "a" cos "C" + "c" + "c" cos "A")/2 = (3"b")/2`

⇒ (a+ c) +(a cos C + c cos A) = 3b

⇒ (a+ c) + b = 3b   ......[By projection rule]

⇒ a + c = 2b

⇒ a, b, care in A.P.