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Sum of cos A/a terms using the cosine rule

This type of question, asked 3 times: 20 Apr 2025 S1, 20 Apr 2025 S2, 25 Apr 2025 S1. All 3 questions below, oldest first.

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  1. Question 1

    20 Apr 2025 S1

    141
    In a triangle ABC , with usual notations if 2cos⁡Aa+cos⁡Bb+2cos⁡Cc=abc+bca\frac{2\cos A}{a}+\frac{\cos B}{b}+\frac{2\cos C}{c}=\frac{a}{bc}+\frac{b}{ca} then ∠A=\angle A=

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  2. Question 2

    20 Apr 2025 S2

    119
    In a triangle ABCABC, the sides a,b,ca,b,c are such that they are the roots of the equation x3−11x2+38x−40=0x^{3}- 11x^{2}+ 38x- 40 = 0 Then cos⁡Aa+cos⁡Bb+cos⁡Cc=\frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=

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  3. Question 3

    25 Apr 2025 S1

    140
    In a triangle ABC, with usual notations, 2cos⁡Aa+cos⁡Bb+2cos⁡Cc=abc+bca\frac{2\cos A}{a}+\frac{\cos B}{b}+\frac{2\cos C}{c}=\frac{a}{bc}+\frac{b}{ca}. Then ∠A=\angle A=

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