PYQ Vault

Given a trig ratio in letters (a/b, p/q, sin/x = cos/y), express another ratio in those letters

This type of question, asked 3 times: 15 Nov 2020 Tier II, 20 Jan 2025 Tier II, 18 Jan 2026 Tier II. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    15 Nov 2020 Tier II

    46
    If sec⁡θ=ab\sec\theta = \frac{a}{b}, b≠0b \ne 0, then 1−tan⁡2θ2−sin⁡2θ=?\frac{1 - \tan^2\theta}{2 - \sin^2\theta} = ?

    Tap an option to check your answer.

  2. Question 2

    20 Jan 2025 Tier II

    19
    If cos⁡27∘=pq\cos 27^\circ = \frac{p}{q}, then find the value of cosec⁡27∘−cos⁡63∘\operatorname{cosec} 27^\circ - \cos 63^\circ.

    Tap an option to check your answer.

  3. Question 3

    18 Jan 2026 Tier II

    30
    If sin⁡θx=cos⁡θy\frac{\sin \theta}{x} = \frac{\cos \theta}{y}, then sin⁡θ−cos⁡θ\sin \theta - \cos \theta is:

    Tap an option to check your answer.