PYQ Vault
EbooksTutor

Find theta from a simple equation in sin, cos, tan (standard angle), then evaluate an expression

This type of question, asked 3 times: 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 8 Aug 2022 Tier II. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    29 Jan 2022 Tier II

    6
    If 3tan⁡θ=23sin⁡θ3\tan\theta = 2\sqrt{3}\sin\theta, 0∘<θ<90∘0^\circ < \theta < 90^\circ, then the value of cosec22θ+cot⁡22θsin⁡2θ+tan⁡22θ\frac{\text{cosec}^2 2\theta + \cot^2 2\theta}{\sin^2\theta + \tan^2 2\theta} is:

    Tap an option to check your answer.

  2. Question 2

    29 Jan 2022 Tier II

    48
    If 7sin⁡2θ+4cos⁡2θ=57\sin^2\theta + 4\cos^2\theta = 5 and θ\theta lies in the first quadrant, then what is the value of 3sec⁡θ+tan⁡θ2cot⁡θ−3cos⁡θ\frac{\sqrt{3}\sec\theta + \tan\theta}{\sqrt{2}\cot\theta - \sqrt{3}\cos\theta}?

    Tap an option to check your answer.

  3. Question 3

    3 Feb 2022 Tier II

    71
    If sin⁡2θcos⁡2θ−3cos⁡θ+2=1\frac{\sin^2\theta}{\cos^2\theta - 3\cos\theta + 2} = 1, θ\theta lies in the first quadrant, then the value of tan⁡2θ2+sin⁡2θ2tan⁡θ+sin⁡θ\frac{\tan^2\frac{\theta}{2} + \sin^2\frac{\theta}{2}}{\tan\theta + \sin\theta} is:

    Tap an option to check your answer.

  4. Question 4

    8 Aug 2022 Tier II

    44
    If 3tan⁡θ=3sin⁡θ\sqrt{3}\tan\theta = 3\sin\theta , then what is the value of sin⁡2θ−cos⁡2θ\sin^2\theta - \cos^2\theta?

    Tap an option to check your answer.