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(a - b)^2 cos^2(C/2) + (a + b)^2 sin^2(C/2) in terms of the sides

The same question, asked 2 times: 10 May 2024 S2*, 13 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2024 S2

    110
    In a triangle ABC, with usual notations, if c=4c=4, then value of (a−b)2cos⁡2 ⁣C2+(a+b)2sin⁡2 ⁣C2(a-b)^2\cos^2\!\frac{C}{2}+(a+b)^2\sin^2\!\frac{C}{2} is

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  2. Question 2

    13 Apr 2026 S1

    65
    With usual notations, in △ABC\triangle ABC, (b−c)2cos⁡2A2+(b+c)2sin⁡2A2=(b - c)^2\cos^2\dfrac{A}{2} + (b + c)^2\sin^2\dfrac{A}{2} =

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