If in a triangle ABC , a ^2 ≤ft( C/2 ) + c ^2 ≤ft( A/2 ) = 3b/2 , then the sides a, b and c : - Mathematics MCQ AIEEE-CBSE-ENG-03 2026 | ExamTest.live

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If in a triangle A BC, a cos^{2} (\frac{C}{2}) + c cos^{2} (\frac{A}{2}) = \frac{3 b}{2}, then the sides a, b and c :

Solution & Step-by-step Explanation

Use the identity cos^{2} (θ /2) = \frac{1 + c o s θ}{2} : a (\frac{1 + cos C}{2}) + c (\frac{1 + cos A}{2}) = \frac{3 b}{2} a + a cos C + c + c cos A = 3 b (a + c) + (a cos C + c cos A) = 3 b By projection formula, a cos C + c cos A = b .Substituting this: (a + c) + b = 3 b a + c = 2 b This implies a, b, c are in A.P.

Try it yourself before checking the explanation above.

If in a triangle A BC, a cos^{2} (\frac{C}{2}) + c cos^{2} (\frac{A}{2}) = \frac{3 b}{2}, then the sides a, b and c :

are in A.P.

are in G.P.

are in H.P.

satisfy a + b = c

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