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tan x + cot x = 2 (or sec x cosec x = 2) forces tan x = 1

This type of question, asked 3 times: CDS 2 2016, CDS 1 2018, CDS 2 2023. All 3 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    81
    If tan⁡2x+1tan⁡2x=2\tan^2 x + \frac{1}{\tan^2 x} = 2 and 0∘<x<90∘0^\circ < x < 90^\circ, then what is the value of xx ?

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  2. Question 2

    CDS 1 2018

    60
    If sec⁡x cosec x=2\sec x \,\mathrm{cosec}\, x = 2, then what is tan⁡nx+cot⁡nx\tan^n x + \cot^n x equal to ?

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  3. Question 3

    CDS 2 2023

    70
    If tan⁡A+cot⁡A=2\tan A + \cot A = 2, where 0<A<90∘0 < A < 90^\circ, then what is the value of tan⁡2A+tan⁡3A+tan⁡4A+....+tan⁡nA\tan^2 A + \tan^3 A + \tan^4 A + .... + \tan^n A ?

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