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(1 + tan A)(1 + tan B) type expressions when A + B = 45 or 225 degrees

This type of question, asked 2 times: 15 May 2023 S2, 20 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    15 May 2023 S2

    150
    If A+B=225∘A+B=225^\circ, then cot⁡A1+cot⁡A⋅cot⁡B1+cot⁡B\frac{\cot A}{1+\cot A}\cdot\frac{\cot B}{1+\cot B}, if it exists, is equal to

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  2. Question 2

    20 Apr 2026 S2

    54
    If x+y=π4x + y = \dfrac{\pi}{4}, then (1+tan⁡x)(1+tan⁡y)=(1 + \tan x)(1 + \tan y) =

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