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← Bihar Board Class 12 PYQ

Inverse Trigonometric Functions

Bihar Board Class 12 · Mathematics · 106 past questions

  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. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\tan^{-1}\dfrac{x}{y} - \tan^{-1}\dfrac{x-y}{x+y} =$
  3. Q3 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $|x| \le 1$, $\cos^{-1}\left(\dfrac{1-x^2}{1+x^2}\right) =$
  4. Q4 2026 Set A2026 Set F
    Prove that $\tan^{-1} 1+\tan^{-1} 2+\tan^{-1} 3=\pi$.
  5. Q5 2026 Set A2026 Set H2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    Find the value of $2\tan^{-1}\frac{1}{3}+\tan^{-1}\frac{1}{7}$.
  6. Q6 2026 Set A
    Prove that $\sec^2(\tan^{-1} 2)+\operatorname{cosec}^2(\cot^{-1} 3)=15$.
  7. Q7 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\tan^{-1}2 + \tan^{-1}3 =$
  8. Q8 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\tan^{-1}\left(-\dfrac{1}{\sqrt{3}}\right) =$
  9. Q9 2026 Set A2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $2\tan^{-1}\dfrac{1}{3} =$
  10. Q10 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set J2024 Set J2024 Set D
    $\cos^{-1}\left(\cos\dfrac{7\pi}{6}\right) =$
  11. Q11 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    If $|x| \le 1$, then $\tan(\cos^{-1}x) =$
  12. Q12 2026 Set B2026 Set D
    $\tan^{-1}(1) + \cos^{-1}(-\frac{1}{2}) + \sin^{-1}(-\frac{1}{2}) =$
  13. Q13 2026 Set C
    $\frac{d}{dx}(\tan^{-1}\sqrt{x} + \cot^{-1}\sqrt{x}) =$
  14. Q14 2026 Set C
    $\frac{d}{dx}(2\tan^{-1}x) =$
  15. Q15 2026 Set E
    Find the value of $2\tan^{-1}\frac13+\tan^{-1}\frac17$.
  16. Q16 2026 Set E2026 Set C2026 Set D
    $\sin(\cos^{-1}\frac{3}{5}) =$
  17. Q17 2026 Set F2026 Set B2026 Set D
    $\cos^{-1}(\cos\frac{7\pi}{6}) =$
  18. Q18 2026 Set F
    $\sin(\cos^{-1} 3/5) =$
  19. Q19 2026 Set F
    $\tan^{-1}(1)+\cos^{-1}(-\frac12)+\sin^{-1}(-\frac12) =$
  20. Q20 2026 Set H2026 Set E2026 Set C2026 Set B2026 Set F2026 Set J2026 Set D2019 Set F
    Prove that $\sec^2(\tan^{-1}2) + \operatorname{cosec}^2(\cot^{-1}3) = 15$
  21. Q21 2026 Set H2026 Set E2026 Set C2026 Set D2026 Set J2026 Set B
    Prove that $\tan^{-1}1+\tan^{-1}2+\tan^{-1}3=\pi$.
  22. Q22 2026 Set H
    $2\tan^{-1}\frac13 =$
  23. Q23 2026 Set H
    $\tan^{-1}(1)+\cos^{-1}\left(-\frac12\right)+\sin^{-1}\left(-\frac12\right) =$
  24. Q24 2026 Set J2026 Set A2026 Set B2026 Set H
    $\sin(\cos^{-1}3/5) =$
  25. Q25 2026 Set J2026 Set A2026 Set C2026 Set E
    $\tan^{-1}(1) + \cos^{-1}\left(-\dfrac{1}{2}\right) + \sin^{-1}\left(-\dfrac{1}{2}\right)$
  26. Q26 2025
    Find the value of…
  27. Q27 2025
    $\tan^{-1}\left(\tan\dfrac{3\pi}{4}\right)$
  28. Q28 2025
    $\cos^{-1}\left(\dfrac{-1}{\sqrt{2}}\right) =$
  29. Q29 20252025 Set A2025 Set E
    $\tan^{-1}(-\sqrt{3}) =$
  30. Q30 2025
    $\sin\left[\dfrac{\pi}{3} - \sin^{-1}\left(\dfrac{-1}{2}\right)\right] =$
  31. Q31 2025
    $\sin(\tan^{-1}x) =$, $|x| < 1$
  32. Q32 2025
    $\sin^{-1}\sin\left(\dfrac{3\pi}{5}\right) =$
  33. Q33 2025
    Domain of $\text{cosec}^{-1}x$ is
  34. Q34 2025
    $\sin^{-1}\left(\dfrac{-1}{2}\right) + \cos^{-1}\left(\dfrac{\sqrt{3}}{2}\right) =$
  35. Q35 2025
    If $\cos^{-1}\alpha + \cos^{-1}\beta + \cos^{-1}\gamma = 3\pi$, then find the value of…
  36. Q36 2025
    Solve the equation $\cos(\tan^{-1}x) = \sin\left(\cot^{-1}\frac{3}{4}\right)$.
  37. Q37 2025
    Prove that $\sin^{-1}\frac{5}{13} + \cos^{-1}\frac{3}{5} = \tan^{-1}\frac{63}{16}$.
  38. Q38 2025 Set A2025 Set E
    $\cot^{-1}\left(\tan\dfrac{\pi}{7}\right) =$
  39. Q39 2025 Set A20252025 Set E2021 Set J2021 Set I
    $\tan^{-1}\sqrt{3} - \cot^{-1}(-\sqrt{3}) =$
  40. Q40 2025 Set A2025 Set E
    $\tan\left\{\frac{1}{2}\left(\tan^{-1}x+\tan^{-1}\frac{1}{x}\right)\right\}=$
  41. Q41 2025 Set A2025 Set E
    $\cos^{-1}x+\sec^{-1}\frac{1}{x}=$
  42. Q42 2025 Set A2025 Set E
    $\tan^{-1}\frac{1}{2}+\tan^{-1}\frac{1}{3}=$
  43. Q43 2025 Set A2025 Set E
    $\sin\left\{\sin^{-1}\frac{1}{5}+\cos^{-1}x\right\}=1,\ \Rightarrow x=$
  44. Q44 2024 Set D
    $\cos^{-1}\left(-\frac12\right)=$
  45. Q45 2024 Set D2024 Set J
    $x\in[-1,1]$, $\cos^{-1}x=$
  46. Q46 2024 Set D2024 Set J
    $x\in[-1,1]$, $\sin^{-1}(-x)=$
  47. Q47 2024 Set D
    $\operatorname{cosec}^{-1}x=\ldots\ldots\ldots\ldots$ ; $x\ge1$ or $\le-1$.
  48. Q48 2024 Set D2024 Set J
    $\sin(\cot^{-1}x)=$
  49. Q49 2024 Set D2024 Set J
    Prove that $4(\cot^{-1}3+\cot^{-1}2)=\pi$.
  50. Q50 2024 Set D2024 Set J
    Prove that $\sin^{-1}\frac{4}{5}+\sin^{-1}\frac{5}{13}+\sin^{-1}\frac{16}{65}=\frac{\pi}{2}$.
  51. Q51 2024 Set D2024 Set J
    $\tan\left[\tan^{-1}\dfrac{1}{3}+\tan^{-1}\dfrac{1}{2}\right]=$
  52. Q52 2024 Set D2024 Set J
    $\frac{\pi}{3} - \sin^{-1}\left(-\frac{1}{2}\right) =$
  53. Q53 2024 Set D2024 Set J
    $\tan^{-1}\sqrt{3} - \sec^{-1}(-2) =$
  54. Q54 2024 Set J
    $\cos^{-1}\left(-\dfrac{1}{2}\right)$
  55. Q55 2024 Set J
    $\operatorname{cosec}^{-1}x=\ldots\ldots\ldots$ ; $x\ge1$ or $\le-1$.
  56. Q56 2024 Set J
    $\frac{d}{dx}(\sec^{-1}x+\operatorname{cosec}^{-1}x) =$
  57. Q57 2023
    $|x| \le 1$, $2\tan^{-1}x =$
  58. Q58 20232023 Set E
    $x \in R, \cot^{-1}x =$
  59. Q59 20232023 Set E
    $\tan^{-1}\left(\dfrac{x+y}{1-xy}\right) =$
  60. Q60 2023
    $\sin^{-1}\left(\sin\dfrac{2\pi}{3}\right) =$
  61. Q61 20232023 Set E
    $\sin\left(\sin^{-1}\frac{1}{2}\right) =$
  62. Q62 20232023 Set E
    $\sin^{-1}x + \sin^{-1}y =$
  63. Q63 2023
    $x \in [-1, 1], \sin[2(\sin^{-1}x + \cos^{-1}x)] =$
  64. Q64 2023
    $x \in R, \text{cosec}(\tan^{-1}x + \cot^{-1}x) =$
  65. Q65 2023
    $|x| \ge 1, \tan\left[\dfrac{2}{3}(\tan^{-1}x + \cot^{-1}x)\right] =$
  66. Q66 2023 Set E
    $x \in [-1, 1]$, $\sin\left[2\left(\sin^{-1}x + \cos^{-1}x\right)\right] =$
  67. Q67 2023 Set E
    $x \in R$, $\operatorname{cosec}\left(\tan^{-1}x + \cot^{-1}x\right) =$
  68. Q68 2023 Set E
    $|x| \geq 1$, $\tan\left[\frac{2}{3}\left(\tan^{-1}x + \cot^{-1}x\right)\right] =$
  69. Q69 2023 Set E
    $|x|\le 1,\ 2\tan^{-1}x=$
  70. Q70 2023 Set E
    Find the principal value of $\mathrm{cosec}^{-1}\,2$.
  71. Q71 2023 Set E
    $\sin^{-1}\left(\sin\dfrac{2\pi}{3}\right)$
  72. Q72 2021 Set I
    $\sin(\sec^{-1}x+\operatorname{cosec}^{-1}x) =$
  73. Q73 2021 Set I
    $2\tan^{-1}\dfrac13+\tan^{-1}\dfrac17 =$
  74. Q74 2021 Set I
    $\operatorname{cosec}^{-1}(-x) =$
  75. Q75 2021 Set I
    $\cos^{-1}(2x) + \sin^{-1}(2x) = \ldots\ldots\ldots,\ 2x \in [-1, 1]$
  76. Q76 2021 Set I
    $\cot^{-1}\dfrac{1}{x} = \ldots\ldots\ldots\ (x > 0)$
  77. Q77 2021 Set J2021 Set I2018
    Prove that…
  78. Q78 2021 Set J
    $\operatorname{cosec}^{-1}(2)$
  79. Q79 2021 Set J2021 Set I
    $\cos^{-1}\dfrac{1-x^2}{1+x^2} = \ldots\ldots\ldots\ldots,\ (|x|\le 1)$
  80. Q80 2021 Set J2021 Set I
    $3\sin^{-1}x = \ldots\ldots\ldots\ldots,\ |x|\le\dfrac12$
  81. Q81 2021 Set J2021 Set I
    $\tan^{-1} 1 =$
  82. Q82 2021 Set J2021 Set I
    $\cos(\sec^{-1} x + \operatorname{cosec}^{-1} x) =$
  83. Q83 2021 Set J
    $\cos^{-1}(2x)+\sin^{-1}(2x)=$ ............, $2x\in[-1,1]$
  84. Q84 2021 Set J2021 Set I
    $\sin^{-1}(-x)=$
  85. Q85 2021 Set J
    $\cot^{-1}\frac{1}{x}=$ ............, $(x>0)$
  86. Q86 2021 Set J
    $2\tan^{-1}\frac{1}{3} + \tan^{-1}\frac{1}{7} =$
  87. Q87 2019 Set F
    If $-1 < x < 1$, then $2\tan^{-1}x = ?$
  88. Q88 2019 Set F
    $\sin^{-1}\frac{1}{x} = ?$
  89. Q89 2019 Set F
    $\sin^{-1}\left(\dfrac{1}{\sqrt2}\right)=\ ?$
  90. Q90 2019 Set F
    $\tan^{-1}x + \cot^{-1}x = ?$
  91. Q91 2018
    $\cos^{-1}(2x-1) =$
  92. Q92 2018
    $2\cot^{-1}3+\cos^{-1}7=$
  93. Q93 2018
    $\tan^{-1}(1)+\cos^{-1}\left(\frac{-1}{2}\right)+\sin^{-1}\left(\frac{-1}{2}\right)=$
  94. Q94 2018
    Prove that $\sin^{-1}\frac{3}{5}-\cos^{-1}\frac{12}{13}=\sin^{-1}\frac{16}{65}$
  95. Q95 2017
    $\tan^{-1}(1) = \ldots\ldots$?
  96. Q96 2017
    $\tan^{-1}\frac{1}{2} + \tan^{-1}\frac{1}{4} = \ldots\ldots\ldots\ldots$
  97. Q97 2017
    Prove that $\tan^{-1}x+\cot^{-1}x=\frac{\pi}{2}$
  98. Q98 2016
    The principal value of $\cos^{-1}\left(-\frac{1}{2}\right)$ is
  99. Q99 2016
    $\tan^{-1}x+\cot^{-1}x=$
  100. Q100 20162015
    $\frac{d}{dx}\left(\cos^{-1}x\right)=$
  101. Q101 2016
    $\tan^{-1}\frac{2x}{1-x^2}$
  102. Q102 2016
    Solve for x: $\tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}$
  103. Q103 2015
    The principal value of $\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)$ is
  104. Q104 2015
    $\tan^{-1} x =$
  105. Q105 2015
    $\cos^{-1}\dfrac{1-x^2}{1+x^2} =$
  106. Q106 2015
    Prove that $4\left(\cot^{-1}3+\operatorname{cosec}^{-1}\sqrt{5}\right)=\pi$