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sin t + cos t (or tan t + cot t) given: square to get sin t cos t, then evaluate

This type of question, asked 7 times: CDS 2 2016, CDS 1 2018, CDS 2 2020, CDS 1 2025, CDS 2 2025, CDS 1 2026, CDS 2 2026. All 9 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    71
    If sin⁡θ+cos⁡θ=72\sin\theta + \cos\theta = \frac{\sqrt{7}}{2}, then what is sin⁡θ−cos⁡θ\sin\theta - \cos\theta equal to ?

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  2. Question 2

    CDS 2 2016

    77
    If sin⁡θ+cos⁡θ=1+32\sin\theta + \cos\theta = \frac{1 + \sqrt{3}}{2} where 0<θ<π20 < \theta < \frac{\pi}{2}, then what is tan⁡θ+cot⁡θ\tan\theta + \cot\theta equal to ?

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  3. Question 3

    CDS 1 2018

    62
    If sin⁡A+cos⁡A=p\sin A + \cos A = p and sin⁡3A+cos⁡3A=q\sin^3 A + \cos^3 A = q, then which one of the following is correct ?

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  4. Question 4

    CDS 2 2020

    55
    If sin⁡θ+cos⁡θ=2\sin \theta + \cos \theta = \sqrt{2}, then what is sin⁡6θ+cos⁡6θ+6sin⁡2θcos⁡2θ\sin^6 \theta + \cos^6 \theta + 6 \sin^2 \theta \cos^2 \theta equal to ?

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  5. Question 5

    CDS 2 2020

    57
    If cos⁡47∘+sin⁡47∘=k\cos 47^\circ + \sin 47^\circ = k, then what is the value of cos⁡247∘−sin⁡247∘\cos^2 47^\circ - \sin^2 47^\circ ?

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  6. Question 6

    CDS 1 2025

    31
    If sin⁡α+cos⁡α=2\sin\alpha + \cos\alpha = \sqrt{2}, where 0<α<π20 < \alpha < \frac{\pi}{2}, then what is sin⁡3α−cos⁡3α\sin^3\alpha - \cos^3\alpha equal to ?

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  7. Question 7 (case study, 2 parts)

    CDS 2 2025

    Let sin⁡θ+cos⁡θ=p\sin\theta + \cos\theta = p and sec⁡θ+cosec θ=q\sec\theta + \mathrm{cosec}\,\theta = q, where p≠1p \ne 1.
    49
    What is the relation between pp and qq?

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    50
    What is tan⁡θ+cot⁡θ\tan\theta + \cot\theta equal to?

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  8. Question 8 (case study, 2 parts)

    CDS 1 2026

    For the next two (02) items that follow : Let 12(tan⁡θ+cot⁡θ)=2512(\tan\theta + \cot\theta) = 25, where 45∘<θ<90∘45^\circ < \theta < 90^\circ.
    91
    What is a value of (sin⁡θ−cos⁡θ)(\sin\theta - \cos\theta) ?

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    92
    What is a value of (cosec⁡θ+sec⁡θ)(\operatorname{cosec}\theta + \sec\theta) ?

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  9. Question 9

    CDS 2 2026

    49
    If (cos⁡35∘+cos⁡55∘)=p(\cos 35^\circ + \cos 55^\circ) = p, then what is sin⁡35∘⋅cos⁡35∘\sin 35^\circ \cdot \cos 35^\circ equal to ?

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