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Half-angle expressions in terms of s and the area

This type of question, asked 3 times: 23 Apr 2025 S1, 18 Apr 2026 S2, 13 May 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    23 Apr 2025 S1

    119
    In a triangle ABC with usual notations, cot⁡A2+cot⁡B2+cot⁡C2=\cot\frac{A}{2}+ \cot\frac{B}{2}+ \cot\frac{C}{2}=

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  2. Question 2

    18 Apr 2026 S2

    62
    In △ABC\triangle ABC, with usual notations, if Δ\Delta denotes the area of triangle ABCABC then the value of 2s(b+c−a)tan⁡(A2)2s(b + c - a)\tan\left(\dfrac{A}{2}\right) is equal to …\ldots

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  3. Question 3

    13 May 2026 S2

    56
    In △ABC\triangle ABC, with usual notations, the value of csc⁡⁡(A2)csc⁡⁡(B2)csc⁡⁡(C2)\operatorname{\csc}\left(\dfrac{A}{2}\right)\operatorname{\csc}\left(\dfrac{B}{2}\right)\operatorname{\csc}\left(\dfrac{C}{2}\right) is:

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