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a sin^2 t + b cos^2 t = c: find tan t

This type of question, asked 2 times: CDS 1 2017, CDS 2 2021. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2017

    66
    If 7sin⁡2x+3cos⁡2x=47 \sin^2 x + 3 \cos^2 x = 4, 0<x<90∘0 < x < 90^\circ, then what is the value of tan⁡x\tan x ?

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  2. Question 2

    CDS 2 2021

    47
    If 14sin⁡2θ+10cos⁡2θ=1114\sin^2\theta+10\cos^2\theta=11 where 0∘<θ<90∘0^\circ<\theta<90^\circ, then what is the value of tan⁡θ+cot⁡θ\tan\theta+\cot\theta ?

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