PYQ Vault
EbooksTutor

Values of a parameter for which a trig equation has a solution (range of the expression)

This type of question, asked 4 times: 2021 Paper 25, 29 Jan 2023, 27 Jan 2024, 5 Apr 2026 S1. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 25

    82
    The number of integral values of ' kk ' for which the equation 3sin⁡x+4cos⁡x=k+13\sin x + 4\cos x = k + 1 has a solution, k∈Rk \in R is

  2. Question 2

    29 Jan 2023

    153
    The set of all values of λ\lambda for which the equation cos⁡22x−2sin⁡4x−2cos⁡2x=λ\cos^{2}2x - 2\sin^{4}x - 2\cos^{2}x = \lambda has a real solution xx, is

    Tap an option to check your answer.

  3. Question 3

    27 Jan 2024

    87
    Let the set of all a∈Ra \in R such that the equation cos⁡2x+asin⁡x=2a−7\cos2x + a\sin x = 2a - 7 has a solution be [p,q]\lbrack p,q\rbrack and r=tan⁡9∘−tan⁡27∘−1cot⁡63∘+tan⁡81∘r = \tan9^{\circ}- \tan27^{\circ}-\frac{1}{\cot63^{\circ}}+ \tan81^{\circ}, then pqr is equal to

  4. Question 4

    5 Apr 2026 S1

    62
    The sum of all the integral values of p such that the equation 3sin⁡2x+12cos⁡x−3=p,x∈R3\sin^{2}x+ 12\cos x- 3 =p,x\in R, has at least one solution, is :

    Tap an option to check your answer.