In ∆ A B C , with usual notations, if a , b , c are in A . P . then a cos 2 ⁡ C 2 + c cos 2 ⁡ A 2 =

Question

In ∆ A B C , with usual notations, if a , b , c are in A . P . then a cos 2 ⁡ C 2 + c cos 2 ⁡ A 2 =, 3 a 2, 3 c 2, 3 b 2, 3 a b c 2

MARKS App · Accepted Answer

Since a , b , c are in A . P . ⇒ 2b = a + c = a 2 2 cos 2 C 2 + c 2 2 cos 2 A 2 = a 2 1 + cos C + c 2 1 + cos A = 1 2 a + a cos C + c + c cos A = 1 2 a + c + b (using projection formula) = 1 2 2 b + b ( ∵ a, b, c are in A.P.) = 3b 2

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