PYQ Vault

Product of tan or cot of two half-angles in terms of the sides (tan(A/2) tan(C/2) = (s - b)/s)

This type of question, asked 6 times: 20 Apr 2025 S1, 20 Apr 2025 S2, 21 Apr 2025 S2, 22 Apr 2025 S2, 15 Apr 2026 S1, 12 May 2026 S1. All 6 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    20 Apr 2025 S1

    144
    In a triangle ABC with usual notations, if a,b,ca,b,c are in arithmetic progression, then, tan⁡A2⋅tan⁡C2=\tan\frac{A}{2}\cdot \tan\frac{C}{2}=

    Tap an option to check your answer.

  2. Question 2

    20 Apr 2025 S2

    124
    In a triangle ABC, with usual notations, 3b=a+c3b=a+c, then cot⁡A2⋅cot⁡C2=\cot\frac{A}{2}\cdot \cot\frac{C}{2}=

    Tap an option to check your answer.

  3. Question 3

    21 Apr 2025 S2

    132
    In a triangle ABC , with usual notations, tan⁡(A2)=56,tan⁡(C2)=25\tan\left( \frac{A}{2} \right)=\frac{5}{6},\tan\left( \frac{C}{2} \right)=\frac{2}{5}, then

    Tap an option to check your answer.

  4. Question 4

    22 Apr 2025 S2

    135
    In a triangle ABC with usual notations, if 3a=b+c3a = b + c, then cot⁡B2⋅cot⁡C2=\cot\frac{B}{2}\cdot \cot\frac{C}{2}=

    Tap an option to check your answer.

  5. Question 5

    15 Apr 2026 S1

    64
    In △ABC\triangle ABC with usual notations, if 1+tan⁡(A2)tan⁡(B2)=ks1 + \tan\left(\dfrac{A}{2}\right)\tan\left(\dfrac{B}{2}\right) = \dfrac{k}{s} (where ss is the semi-perimeter), then the value of kk is...

    Tap an option to check your answer.

  6. Question 6

    12 May 2026 S1

    55
    In ΔABC\Delta ABC, with usual notations, if 1−tan⁡A2⋅tan⁡C2=bk1 - \tan\dfrac{A}{2} \cdot \tan\dfrac{C}{2} = \dfrac{b}{k}, then k=k = ...

    Tap an option to check your answer.