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Projection rule a = b cos C + c cos B to simplify an expression

This type of question, asked 3 times: 4 May 2023 S2, 15 May 2023 S2, 20 Apr 2025 S1. All 3 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    118
    If (a+b)cos⁡C+(b+c)cos⁡A+(c+a)cos⁡B=72(a+b)\cos C+(b+c)\cos A+(c+a)\cos B=72 and if a=18,b=24a=18, b=24, then area of the triangle ABC is

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  2. Question 2

    15 May 2023 S2

    143
    In a triangle ABC, with usual notations, cos⁡B+cos⁡Cb+c+cos⁡Aa\frac{\cos B+\cos C}{b+c}+\frac{\cos A}{a} has the value

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  3. Question 3

    20 Apr 2025 S1

    147
    With usual notations, in a triangle ABCABC, if θ\theta is any real number, then acos(B−θ)+bcos(A+θ)acos(B-\theta) +bcos(A+\theta) is

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