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Evaluate an expression of standard-angle values (30, 45, 60, 90)

This type of question, asked 12 times: 14 Jul 2023 S3, 17 Jul 2023 S2, 18 Jul 2023 S4, 20 Jul 2023 S3, 25 Jul 2023 S3, 26 Jul 2023 S1, 11 Sep 2024 S2, 13 Sep 2024 S1, 13 Sep 2024 S3, 23 Sep 2024 S3, 25 Sep 2024 S3, 21 Sep 2025 S3. All 12 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S3

    68
    What is the value of sin⁡30∘+cos⁡30∘+tan⁡30∘\sin 30^\circ + \cos 30^\circ + \tan 30^\circ

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  2. Question 2

    17 Jul 2023 S2

    66
    If tan⁡π6+sec⁡π6=x\tan\frac{\pi}{6} + \sec\frac{\pi}{6} = x, then find x.

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  3. Question 3

    18 Jul 2023 S4

    57
    Find the value of the given expression. 43tan⁡245∘+3cos⁡230∘−2sec⁡230∘−34cot⁡260∘\frac{4}{3}\tan^2 45^\circ + 3\cos^2 30^\circ - 2\sec^2 30^\circ - \frac{3}{4}\cot^2 60^\circ

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  4. Question 4

    20 Jul 2023 S3

    67
    Find the value of 23tan⁡260∘+3cos⁡230∘−2sec⁡230∘−34cot⁡260∘\frac{2}{3} \tan^2 60^\circ + 3 \cos^2 30^\circ - 2 \sec^2 30^\circ - \frac{3}{4} \cot^2 60^\circ.

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  5. Question 5

    25 Jul 2023 S3

    68
    What is the value of 53cos⁡60∘tan⁡30∘−3cos⁡0∘+3cos⁡245∘+2sin⁡260∘5\sqrt{3}\cos 60^\circ \tan 30^\circ - 3\cos 0^\circ + 3\cos^2 45^\circ + 2\sin^2 60^\circ?

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  6. Question 6

    26 Jul 2023 S1

    67
    The value of cosec 30∘−cos⁡60∘\text{cosec}\ 30^\circ - \cos 60^\circ is:

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  7. Question 7

    11 Sep 2024 S2

    58
    Find the value of: [43tan⁡260∘+3cos⁡230∘−2sec⁡230∘−34cot⁡260∘]÷[sin⁡60∘cos⁡30∘−cos⁡60∘sin⁡30∘]\left[\frac{4}{3}\tan^2 60^\circ + 3\cos^2 30^\circ - 2\sec^2 30^\circ - \frac{3}{4}\cot^2 60^\circ\right] \div \left[\sin 60^\circ \cos 30^\circ - \cos 60^\circ \sin 30^\circ\right]

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  8. Question 8

    13 Sep 2024 S1

    61
    If p(3+cot⁡30∘)=tan⁡360∘−2sin⁡60∘p(\sqrt{3} + \cot 30^\circ) = \tan^3 60^\circ - 2\sin 60^\circ, then the value of p is:

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  9. Question 9

    13 Sep 2024 S3

    63
    The value of (cosec⁡Acosec⁡A−1+cosec⁡Acosec⁡A+1)(sec⁡Asec⁡A−1+sec⁡Asec⁡A+1)−1\left(\frac{\operatorname{cosec}A}{\operatorname{cosec}A - 1} + \frac{\operatorname{cosec}A}{\operatorname{cosec}A + 1}\right)\left(\frac{\sec A}{\sec A - 1} + \frac{\sec A}{\sec A + 1}\right)^{-1}, when A=60∘A = 60^\circ is:

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  10. Question 10

    23 Sep 2024 S3

    66
    The value of sin⁡2θ−2sin⁡4θ2cos⁡4θ+cos⁡2θ\frac{\sin^2\theta - 2\sin^4\theta}{2\cos^4\theta + \cos^2\theta} at θ=45∘\theta = 45^\circ is:

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  11. Question 11

    25 Sep 2024 S3

    63
    What is the value of (53−cosec 60∘)\left(\frac{5}{\sqrt{3}} - \text{cosec } 60^\circ\right)?

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  12. Question 12

    21 Sep 2025 S3

    69
    Find the value of sin⁡290∘+cos⁡260∘\sin^2 90^\circ + \cos^2 60^\circ.

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