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Question: If in ∆ABC, cos(A – C) cos B + cos 2B = 0 then a<sup>2</sup>, b<sup>2</sup>, c<sup>2</sup> are in-...

If in ∆ABC, cos(A – C) cos B + cos 2B = 0 then a2, b2, c2 are in-

A

A.P.

B

G.P.

C

H.P.

D

None

Answer

A.P.

Explanation

Solution

–cos(A – C) cos(A + C) + 1 – 2sin2B = 0

–[cos2A – sin2C] + 1 – 2sin2B = 0

sin2A + sin2C = 2 sin2B

∴ a2 + c2 = 2b2

a2, b2, c2 are in A.P.