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Square and add two given relations to eliminate t

This type of question, asked 4 times: CDS 1 2017, CDS 1 2021, CDS 2 2021, CDS 1 2026. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2017

    68
    If x=acos⁡θ+bsin⁡θx = a \cos \theta + b \sin \theta and y=asin⁡θ−bcos⁡θy = a \sin \theta - b \cos \theta, then what is x2+y2x^2 + y^2 equal to ?

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  2. Question 2

    CDS 1 2021

    58
    If 6+8tan⁡θ=sec⁡θ6 + 8\tan\theta = \sec\theta and 8−6tan⁡θ=ksec⁡θ8 - 6\tan\theta = k\sec\theta, then what is the value of k2k^2?

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  3. Question 3

    CDS 2 2021

    55
    If x=psin⁡Acos⁡Bx=p\sin A\cos B, y=psin⁡Asin⁡By=p\sin A\sin B and z=pcos⁡Az=p\cos A, then what is the value of x2+y2+z2x^2+y^2+z^2 ?

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  4. Question 4

    CDS 2 2021

    56
    If x=msec⁡A+ntan⁡Ax=m\sec A+n\tan A and y=mtan⁡A+nsec⁡Ay=m\tan A+n\sec A, then what is x2−y2x^2-y^2 equal to ?

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  5. Question 5 (case study, 2 parts)

    CDS 1 2026

    For the next two (02) items that follow : p+qcot⁡θ=3cosec⁡θp + q\cot\theta = 3\operatorname{cosec}\theta and q−pcot⁡θ=2cosec⁡θq - p\cot\theta = 2\operatorname{cosec}\theta
    97
    What is p2+q2p^2 + q^2 equal to ?

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    98
    What is tan⁡θ\tan\theta equal to ?

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