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A ratio equals a standard value: find the angle, then evaluate

This type of question, asked 7 times: 14 Jul 2023 S1, 25 Jul 2023 S1, 25 Jul 2023 S3, 17 Sep 2024 S1, 24 Sep 2024 S1, 26 Sep 2024 S2, 19 Sep 2025 S3. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    14 Jul 2023 S1

    68
    If cos⁡θ=32\cos\theta = \frac{\sqrt{3}}{2}, then tan⁡2θcos⁡2θ=?\tan^2\theta\cos^2\theta = ?

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  2. Question 2

    25 Jul 2023 S1

    74
    If cot⁡A=1\cot A = 1, sin⁡B=12\sin B = \frac{1}{\sqrt{2}}, then find the value of sin⁡(A+B)−cot⁡(A+B)\sin(A + B) - \cot(A + B).

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  3. Question 3

    25 Jul 2023 S3

    72
    If cos⁡2θ=34\cos^2\theta = \frac{3}{4}, where θ\theta is an acute angle, then the value of sin⁡(θ+30∘)\sin(\theta + 30^\circ) is:

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  4. Question 4

    17 Sep 2024 S1

    72
    In a right angle Δ\DeltaABC, ∠B=90∘\angle B = 90^\circ, if tan⁡A=1\tan A = 1, then 4sin⁡Acos⁡A4 \sin A \cos A =_________________.

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  5. Question 5

    24 Sep 2024 S1

    57
    If sec⁡θ=2\sec\theta = \sqrt{2}, then cosec θ\text{cosec}\,\theta is equal to:

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  6. Question 6

    26 Sep 2024 S2

    75
    In a Δ\DeltaABC, right angled at B if tan⁡C=3\tan C = \sqrt{3}, then find sin⁡2C+cos⁡2C1+cot⁡2C\frac{\sin^2 C + \cos^2 C}{1 + \cot^2 C}.

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  7. Question 7

    19 Sep 2025 S3

    64
    If cot⁡A=3\cot A = \sqrt{3}, what is the value of (1+sin⁡A)(1+cos⁡A)(1 + \sin A)(1 + \cos A)?

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