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Inverse Trigonometric Functions

Bihar Board Class 12 · Mathematics · 106 past questions

65 of 106 · show all

  1. Q1 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $x \in R$, $\cot(\tan^{-1}x + \cot^{-1}x) =$
  2. Q3 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $|x| \le 1$, $\cos^{-1}\left(\dfrac{1-x^2}{1+x^2}\right) =$
  3. Q8 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\tan^{-1}\left(-\dfrac{1}{\sqrt{3}}\right) =$
  4. Q9 2026 Set A2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $2\tan^{-1}\dfrac{1}{3} =$
  5. Q10 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set J2024 Set J2024 Set D
    $\cos^{-1}\left(\cos\dfrac{7\pi}{6}\right) =$
  6. Q12 2026 Set B2026 Set D
    $\tan^{-1}(1) + \cos^{-1}(-\frac{1}{2}) + \sin^{-1}(-\frac{1}{2}) =$
  7. Q13 2026 Set C
    $\frac{d}{dx}(\tan^{-1}\sqrt{x} + \cot^{-1}\sqrt{x}) =$
  8. Q14 2026 Set C
    $\frac{d}{dx}(2\tan^{-1}x) =$
  9. Q16 2026 Set E2026 Set C2026 Set D
    $\sin(\cos^{-1}\frac{3}{5}) =$
  10. Q18 2026 Set F
    $\sin(\cos^{-1} 3/5) =$
  11. Q19 2026 Set F
    $\tan^{-1}(1)+\cos^{-1}(-\frac12)+\sin^{-1}(-\frac12) =$
  12. Q22 2026 Set H
    $2\tan^{-1}\frac13 =$
  13. Q24 2026 Set J2026 Set A2026 Set B2026 Set H
    $\sin(\cos^{-1}3/5) =$
  14. Q28 2025
    $\cos^{-1}\left(\dfrac{-1}{\sqrt{2}}\right) =$
  15. Q29 20252025 Set A2025 Set E
    $\tan^{-1}(-\sqrt{3}) =$
  16. Q33 2025
    Domain of $\text{cosec}^{-1}x$ is
  17. Q34 2025
    $\sin^{-1}\left(\dfrac{-1}{2}\right) + \cos^{-1}\left(\dfrac{\sqrt{3}}{2}\right) =$
  18. Q39 2025 Set A20252025 Set E2021 Set J2021 Set I
    $\tan^{-1}\sqrt{3} - \cot^{-1}(-\sqrt{3}) =$
  19. Q40 2025 Set A2025 Set E
    $\tan\left\{\frac{1}{2}\left(\tan^{-1}x+\tan^{-1}\frac{1}{x}\right)\right\}=$
  20. Q42 2025 Set A2025 Set E
    $\tan^{-1}\frac{1}{2}+\tan^{-1}\frac{1}{3}=$
  21. Q44 2024 Set D
    $\cos^{-1}\left(-\frac12\right)=$
  22. Q45 2024 Set D2024 Set J
    $x\in[-1,1]$, $\cos^{-1}x=$
  23. Q46 2024 Set D2024 Set J
    $x\in[-1,1]$, $\sin^{-1}(-x)=$
  24. Q47 2024 Set D
    $\operatorname{cosec}^{-1}x=\ldots\ldots\ldots\ldots$ ; $x\ge1$ or $\le-1$.
  25. Q51 2024 Set D2024 Set J
    $\tan\left[\tan^{-1}\dfrac{1}{3}+\tan^{-1}\dfrac{1}{2}\right]=$
  26. Q52 2024 Set D2024 Set J
    $\frac{\pi}{3} - \sin^{-1}\left(-\frac{1}{2}\right) =$
  27. Q55 2024 Set J
    $\operatorname{cosec}^{-1}x=\ldots\ldots\ldots$ ; $x\ge1$ or $\le-1$.
  28. Q56 2024 Set J
    $\frac{d}{dx}(\sec^{-1}x+\operatorname{cosec}^{-1}x) =$
  29. Q57 2023
    $|x| \le 1$, $2\tan^{-1}x =$
  30. Q58 20232023 Set E
    $x \in R, \cot^{-1}x =$
  31. Q59 20232023 Set E
    $\tan^{-1}\left(\dfrac{x+y}{1-xy}\right) =$
  32. Q61 20232023 Set E
    $\sin\left(\sin^{-1}\frac{1}{2}\right) =$
  33. Q62 20232023 Set E
    $\sin^{-1}x + \sin^{-1}y =$
  34. Q63 2023
    $x \in [-1, 1], \sin[2(\sin^{-1}x + \cos^{-1}x)] =$
  35. Q64 2023
    $x \in R, \text{cosec}(\tan^{-1}x + \cot^{-1}x) =$
  36. Q65 2023
    $|x| \ge 1, \tan\left[\dfrac{2}{3}(\tan^{-1}x + \cot^{-1}x)\right] =$
  37. Q66 2023 Set E
    $x \in [-1, 1]$, $\sin\left[2\left(\sin^{-1}x + \cos^{-1}x\right)\right] =$
  38. Q67 2023 Set E
    $x \in R$, $\operatorname{cosec}\left(\tan^{-1}x + \cot^{-1}x\right) =$
  39. Q68 2023 Set E
    $|x| \geq 1$, $\tan\left[\frac{2}{3}\left(\tan^{-1}x + \cot^{-1}x\right)\right] =$
  40. Q69 2023 Set E
    $|x|\le 1,\ 2\tan^{-1}x=$
  41. Q70 2023 Set E
    Find the principal value of $\mathrm{cosec}^{-1}\,2$.
  42. Q72 2021 Set I
    $\sin(\sec^{-1}x+\operatorname{cosec}^{-1}x) =$
  43. Q74 2021 Set I
    $\operatorname{cosec}^{-1}(-x) =$
  44. Q75 2021 Set I
    $\cos^{-1}(2x) + \sin^{-1}(2x) = \ldots\ldots\ldots,\ 2x \in [-1, 1]$
  45. Q76 2021 Set I
    $\cot^{-1}\dfrac{1}{x} = \ldots\ldots\ldots\ (x > 0)$
  46. Q79 2021 Set J2021 Set I
    $\cos^{-1}\dfrac{1-x^2}{1+x^2} = \ldots\ldots\ldots\ldots,\ (|x|\le 1)$
  47. Q81 2021 Set J2021 Set I
    $\tan^{-1} 1 =$
  48. Q82 2021 Set J2021 Set I
    $\cos(\sec^{-1} x + \operatorname{cosec}^{-1} x) =$
  49. Q83 2021 Set J
    $\cos^{-1}(2x)+\sin^{-1}(2x)=$ ............, $2x\in[-1,1]$
  50. Q84 2021 Set J2021 Set I
    $\sin^{-1}(-x)=$
  51. Q85 2021 Set J
    $\cot^{-1}\frac{1}{x}=$ ............, $(x>0)$
  52. Q87 2019 Set F
    If $-1 < x < 1$, then $2\tan^{-1}x = ?$
  53. Q88 2019 Set F
    $\sin^{-1}\frac{1}{x} = ?$
  54. Q89 2019 Set F
    $\sin^{-1}\left(\dfrac{1}{\sqrt2}\right)=\ ?$
  55. Q90 2019 Set F
    $\tan^{-1}x + \cot^{-1}x = ?$
  56. Q93 2018
    $\tan^{-1}(1)+\cos^{-1}\left(\frac{-1}{2}\right)+\sin^{-1}\left(\frac{-1}{2}\right)=$
  57. Q95 2017
    $\tan^{-1}(1) = \ldots\ldots$?
  58. Q97 2017
    Prove that $\tan^{-1}x+\cot^{-1}x=\frac{\pi}{2}$
  59. Q98 2016
    The principal value of $\cos^{-1}\left(-\frac{1}{2}\right)$ is
  60. Q99 2016
    $\tan^{-1}x+\cot^{-1}x=$
  61. Q100 20162015
    $\frac{d}{dx}\left(\cos^{-1}x\right)=$
  62. Q101 2016
    $\tan^{-1}\frac{2x}{1-x^2}$
  63. Q103 2015
    The principal value of $\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)$ is
  64. Q104 2015
    $\tan^{-1} x =$
  65. Q105 2015
    $\cos^{-1}\dfrac{1-x^2}{1+x^2} =$