PYQ Vault
EbooksTutor

Given one trig ratio (or two sides) as numbers, find the value of an expression in other ratios

This type of question, asked 5 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 8 Aug 2022 Tier II, 20 Jan 2025 Tier II. All 6 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    15 Nov 2020 Tier II

    49
    In Δ\Delta PQR, ∠Q=90∘\angle Q = 90^\circ. If cot R = 13\frac{1}{3}, then what is the value of sec⁡P(cos⁡R+sin⁡P)cosec R (sin⁡R−cosec P)\frac{\sec P(\cos R + \sin P)}{\text{cosec}\,R\,(\sin R - \text{cosec}\,P)}?

    Tap an option to check your answer.

  2. Question 2

    29 Jan 2022 Tier II

    87
    If sin⁡A=513\sin A = \frac{5}{13} and 7cot⁡B=247\cot B = 24, then the value of (sec⁡Acos⁡B)(cosec Btan⁡A)(\sec A\cos B)(\text{cosec}\,B\tan A) is:

    Tap an option to check your answer.

  3. Question 3

    3 Feb 2022 Tier II

    19
    If cos⁡θ=1213\cos\theta = \frac{12}{13}, then the value of sin⁡θ(1−tan⁡θ)tan⁡θ(1+cosec θ)\frac{\sin\theta(1 - \tan\theta)}{\tan\theta(1 + \text{cosec}\,\theta)} is:

    Tap an option to check your answer.

  4. Question 4

    8 Aug 2022 Tier II

    3
    If sin⁡θ=(9/41)\sin\theta = (9/41), 0∘<θ<90∘0^\circ < \theta < 90^\circ then what is the value of cot⁡θ\cot\theta?

    Tap an option to check your answer.

  5. Question 5

    20 Jan 2025 Tier II

    6
    Let PQR be a right angled triangle, right-angled at R. Let PQ = 29 cm, QR = 21 cm and ∠Q=θ\angle Q = \theta. Find the value of cos⁡2θ−sin⁡2θ\cos^2\theta - \sin^2\theta.

    Tap an option to check your answer.

  6. Question 6

    20 Jan 2025 Tier II

    25
    If sin⁡A=513\sin A = \frac{5}{13}, then find the value of cos⁡A−2tan⁡Asin⁡A+3tan⁡A\frac{\cos A - 2\tan A}{\sin A + 3\tan A}.

    Tap an option to check your answer.