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Equation linear in sin^2 and cos^2 (or cosec^2 and cot^2): solve for tan or the angle

This type of question, asked 5 times: 10 Sep 2024 S3, 12 Sep 2024 S1, 19 Sep 2024 S1, 24 Sep 2024 S3, 18 Sep 2025 S1. All 5 questions below, oldest first.

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  1. Question 1

    10 Sep 2024 S3

    69
    If 7cos⁡2θ+5sin⁡2θ−6=07\cos^2\theta + 5\sin^2\theta - 6 = 0, (0∘<θ<90∘)(0^\circ < \theta < 90^\circ), then what is the value of 1+sec⁡θ+tan⁡θsec⁡θ−tan⁡θ1 + \sqrt{\frac{\sec\theta + \tan\theta}{\sec\theta - \tan\theta}}?

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  2. Question 2

    12 Sep 2024 S1

    71
    If 2cosec⁡2θ+3cot⁡2θ=172\operatorname{cosec}^2\theta + 3\cot^2\theta = 17, then the value of ′θ′'\theta' when 0∘≤θ≤90∘0^\circ \le \theta \le 90^\circ is:

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  3. Question 3

    19 Sep 2024 S1

    72
    If 3sin⁡2θ+5cos⁡2θ=43\sin^2\theta + 5\cos^2\theta = 4 and θ\theta is an acute angle, then the value of tan⁡θ\tan\theta is:

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  4. Question 4

    24 Sep 2024 S3

    75
    If 10sin⁡2θ+6cos⁡2θ=7,0<θ<90∘10\sin^2\theta + 6\cos^2\theta = 7, 0 < \theta < 90^\circ, then find the value of tan⁡θ\tan\theta.

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  5. Question 5

    18 Sep 2025 S1

    72
    If sin⁡2A−cos⁡2A=12\sin^2 A - \cos^2 A = \frac{1}{2}, find the value of cos⁡2A\cos^2 A.

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