Introduction to Trigonometry

Bihar Board Class 10 · Mathematics · 116 past questions

1. Q1 2026

   If $\sin\theta = \frac{45}{53}$ then $\cos\theta =$

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2. Q2 2026

   $\frac{\sin 29^\circ}{\cos 61^\circ} =$

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3. Q3 2026

   Which of the following options is not equal to unity ?

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4. Q4 2026

   The value of $\cos\theta$ in the form of $\sin\theta$ is

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5. Q5 2026

   If $\sec\theta=\text{cosec}\,\theta$ then $\theta =$

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6. Q6 2026

   $\sin^2 30^\circ + \cos^2 60^\circ - \cot^2 45^\circ =$

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7. Q7 2026

   If $\sqrt{3}\tan\theta = 1$ then $\theta =$

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8. Q8 2026

   If $\cot A + \frac{1}{\cot A} = 2$ then $\tan^2 A + \frac{1}{\tan^2 A} =$

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9. Q9 2026

   $\sin^4\theta - \cos^4\theta =$

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10. Q10 2026

    If $\sin\theta+\sin^2\theta=1$ then $\cos^2\theta+\cos^4\theta=$

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11. Q11 2026

    $\dfrac{1+\tan^2 A}{1+\cot^2 A}=$

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12. Q12 2026

    If $\tan\theta+\cot\theta=5$ then $\tan^2\theta+\cot^2\theta=$

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13. Q13 2025

    $\tan 10^\circ \cdot \tan 23^\circ \cdot \tan 80^\circ \cdot \tan 67^\circ =$

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14. Q14 2025

    $7\sec^2 A - 7\tan^2 A =$

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15. Q15 2025

    If $x = a\cos\theta$ and $y = b\sin\theta$ then $b^2x^2 + a^2y^2 =$

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16. Q16 2025

    If $\cos\theta + \cos^2\theta = 1$ then the value of $\sin^2\theta + \sin^4\theta$ is

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17. Q17 2025

    $\frac{1+\tan^2 A}{1+\cot^2 A} =$

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18. Q18 2025

    $\sin(90^\circ - A) =$

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19. Q19 2025

    If $\theta = 45^\circ$ then the value of $\sin\theta + \cos\theta$ is

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20. Q20 2025

    If $A = 30^\circ$ then the value of $\frac{2\tan A}{1-\tan^2 A}$ is

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21. Q21 2025

    If $\tan\theta = \frac{12}{5}$ then the value of $\sin\theta$ is

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22. Q22 2025

    $\frac{\cos 59^\circ}{\sin 31^\circ} \times \frac{\tan 80^\circ}{\cot 10^\circ} =$

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23. Q23 2025

    If $\tan 25^\circ \times \tan 65^\circ = \sin A$ then the value of $A$ is

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24. Q24 2025

    If $\cos\theta = x$ then $\tan\theta =$

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25. Q25 2025

    $(1-\cos^4\theta) =$

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26. Q26 2025

    $1+\cot^2\theta =$

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27. Q27 2025

    Which of the following values is equal to 1 ?

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28. Q28 2025

    $\cos^2 A(1+\tan^2 A) =$

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29. Q29 2025

    $\tan 30^\circ =$

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30. Q30 2025

    $\cos 60^\circ =$

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31. Q31 2025

    $\sin^2 90^\circ - \tan^2 45^\circ =$

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32. Q32 2025

    $(\sin 30° + \cos 30°) - (\sin 60° + \cos 60°) =$

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33. Q33 2024

    If $\sin(20^\circ + \theta) = \cos 30^\circ$ then the value of $\theta$ is

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34. Q34 2024

    If in $\triangle ABC$, $\angle C = 90^\circ$ then $\sin(A + B) =$

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35. Q35 2024

    $\sec^2 23^\circ - \tan^2 23^\circ + 2 =$

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36. Q36 2024

    If $x\cos\theta = 1$, $\tan\theta = y$ then the value of $x^2 - y^2$ is

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37. Q37 2024

    If $\tan\theta = \frac{3}{4}$ then $\sin\theta =$

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38. Q38 2024

    $\sqrt{\frac{1+\cos A}{1-\cos A}} =$

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39. Q39 2024

    $\tan 5^\circ \cdot \tan 25^\circ \cdot \tan 30^\circ \cdot \tan 65^\circ \cdot \tan 85^\circ =$

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40. Q40 2024

    $\cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ =$

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41. Q41 2024

    $\frac{\text{cosec}\,42^\circ}{\sec 48^\circ} \times \frac{\cos 37^\circ}{\sin 53^\circ} =$

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42. Q42 2024

    If $\tan(\alpha+\beta)=\sqrt{3}$ and $\tan\alpha=\dfrac{1}{\sqrt{3}}$ then the value of $\tan\beta$ is

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43. Q43 2024

    $\sqrt{2}\left(\sin\dfrac{\pi}{4}+\cos\dfrac{\pi}{4}\right)=$

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44. Q44 2024

    If $a\cos\theta+b\sin\theta=4$ and $a\sin\theta-b\cos\theta=3$ then the value of $a^2+b^2$ is

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45. Q45 2023

    $\dfrac{\cos 60^\circ + 1}{\cos 60^\circ - 1} =$

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46. Q46 2023

    If $A/5 = 12^\circ$, then the value of $3\,\mathrm{cosec}^2 A$ will be

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47. Q47 2023

    $\sin 54^\circ - \cos 36^\circ =$

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48. Q48 2023

    $\cos 1^\circ \cos 2^\circ \cos 3^\circ \ldots \cos 90^\circ =$

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49. Q49 2023

    The value of $\frac{\cos 37^\circ}{\sin 53^\circ}+\frac{\cot 34^\circ}{\tan 56^\circ}$ is

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50. Q50 2023

    $2(\sin 45^\circ - \cos 45^\circ) =$

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51. Q51 2023

    The value of $7\operatorname{cosec}^2\theta - 7\cot^2\theta$ is

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52. Q52 2023

    If $\sin 48^\circ = p$, then the value of $\tan 48^\circ$ is

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53. Q53 2023

    If $\tan 27^\circ \tan 63^\circ = \sin A$, then the value of $A$ is

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54. Q54 2023

    $\frac{\sin^2(90^\circ-\theta)+\sin^2\theta}{\operatorname{cosec}^2(90^\circ-\theta)-\tan^2\theta} =$

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55. Q55 2023

    $(1-\sin^4\theta)$

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56. Q56 2023

    If $\tan\theta = \frac{15}{8}$, then the value of $\sin\theta$ will be

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57. Q57 2023

    If $(\tan\theta + \cot\theta) = 6$, then the value of $\tan^2\theta + \cot^2\theta$ is

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58. Q58 2023

    If $\sin\theta = \dfrac{\sqrt{3}}{2}$, then the value of $\operatorname{cosec}\theta + \cot\theta$ is

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59. Q59 2023

    If $\sin\theta = \cos\theta$, $0 \leq \theta \leq 90^\circ$, then value of $\theta$ is

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60. Q60 2023

    $\dfrac{\sin 30^\circ + \cos 45^\circ - \tan 60^\circ}{\cot 30^\circ - \sin 45^\circ - \cos 60^\circ} =$

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61. Q61 2023

    $\tan 30^\circ \sin 30^\circ \cot 60^\circ \operatorname{cosec} 30^\circ =$

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62. Q62 2022

    In right $\triangle ABC$, $\angle B=90^\circ$, $AB=12$ cm, $BC=5$ cm and $AC=13$ cm, then $\sin C$ is equal to

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63. Q63 2022

    If $\cos\theta = p$ then the value of $\tan\theta$ is

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64. Q64 2022

    $\frac{1}{\sin\theta} =$

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65. Q65 2022

    $\sec B \times \cos B =$

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66. Q66 2022

    If $\cot\theta = \frac{1}{\sqrt{3}}$ then the value of $\sec\theta$ is

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67. Q67 2022

    If $A = 45^\circ$ then $\sin A + \cos A =$

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68. Q68 2022

    If $2\sin\alpha = 2$ then $\alpha =$

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69. Q69 2022

    $\frac{\tan 21^\circ}{\cot 69^\circ} =$

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70. Q70 2022

    $\frac{\sin 30^\circ}{\cos 30^\circ} \times \cot 30^\circ =$

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71. Q71 2022

    $\frac{1-\tan^2 45^\circ}{1+\tan^2 45^\circ} =$

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72. Q72 2022

    $\tan 60^\circ : \tan 45^\circ =$

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73. Q73 2022

    If $\theta$ and $\phi$ are complementary angles then

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74. Q74 2022

    $\sin^2 75^\circ + \sin^2 15^\circ =$

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75. Q75 2022

    $1+\tan^2\theta =$

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76. Q76 2022

    $2(\sin^2\alpha + \cos^2\alpha) =$

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77. Q77 2022

    $5\operatorname{cosec}^2\theta - 5\cot^2\theta =$

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78. Q78 2022

    If $3\alpha = 180^\circ$ then $\cos\alpha =$

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79. Q79 2022

    If $a\sin\theta = 1$ and $b\cos\theta = 1$ then $\tan\theta =$

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80. Q80 2022

    Whose value is $\frac{1}{\sqrt{3}}$ ?

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81. Q81 2022

    If $\sec\theta + \tan\theta = x$ then $\tan\theta =$

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82. Q82 2022

    $\sin^2\phi + \frac{1}{1+\tan^2\phi} =$

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83. Q83 2020

    $\tan 10^\circ \tan 15^\circ \tan 75^\circ \tan 80^\circ = ?$

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84. Q84 2020

    The length of the shadow of a 12 m high pillar falling on land is $4\sqrt{3}$ m. The angle of elevation of…

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85. Q85 2020

    $\Delta ABC$ is a right angled triangle in which $\angle C = 90^\circ$. The value of $\cos(A+B)$ is

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86. Q86 2020

    $(1 + \tan\theta + \sec\theta)(1 + \cot\theta - \operatorname{cosec}\theta) = ?$

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87. Q87 2020

    $\sin(90^\circ - \theta) =$

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88. Q88 2020

    If $\sec\theta = \frac{13}{12}$, then $\cot\theta$ is equal to

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89. Q89 2020

    $\frac{\sin 63^\circ}{\cos 27^\circ} =$

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90. Q90 2020

    If $\tan\theta = \frac{8}{15}$, then the value of $\text{cosec}\,\theta$ is

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91. Q91 2020

    Value of $2\cos^2 60°$ is

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92. Q92 2020

    $1 + \tan^2\theta =$

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93. Q93 2020

    Which of the following is equal to cosec$\theta$ ?

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94. Q94 2020

    If $2\sin\theta = 1$, then the value of $(3\cot^2\theta + 3)$ will be

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95. Q95 2019

    If A, B, C are angles of a triangle, then $\sin\left(\frac{B+C}{2}\right)$ is equal to -

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96. Q96 2019

    If $\tan\theta = \frac{3}{4}$, then the value of $\sin\theta$ is -

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97. Q97 2019

    $\frac{\sin 18^\circ}{\cos 72^\circ} =$

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98. Q98 2019

    If 5cosθ=3, then the value of 3tanθ will be -

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99. Q99 2019

    $\cos(90^\circ - A) =$

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100. Q100 2019

     $\cos 1^\circ \cos 2^\circ \cos 3^\circ \ldots\ldots\ldots \cos 90^\circ =$

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101. Q101 2019

     If $\sin\theta = \cos\theta$, then $\theta$ is equal to-

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102. Q102 2019

     $\sin^2\theta + \cos^2\theta =$

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103. Q103 2019

     Which of the following is equal to $\cot\theta$?

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104. Q104 2019

     Value of $\tan^2 60^\circ$ is-

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105. Q105 2018

     If $\sqrt{3}\tan\theta = 3\sin\theta$, then $\sin^2\theta - \cos^2\theta$ is equal to -

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106. Q106 2018

     If $7\sin^2\theta + 3\cos^2\theta = 4$, then $\sec\theta + \operatorname{cosec}\theta$ is equal to -

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107. Q107 2018

     If $5\cot\theta = 3$, then $\frac{5\sin\theta - 3\cos\theta}{4\sin\theta + 3\cos\theta}$ is equal to -

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108. Q108 2018

     If $\sin x^\circ = \sin\alpha$, then $\alpha$ is -

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109. Q109 2018

     The value of $\tan 15^\circ \cdot \tan 20^\circ \cdot \tan 70^\circ \cdot \tan 75^\circ$ -

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110. Q110 2018

     At 4:24 pm, how many degrees has the hour hand of a clock moved from its position at noon?

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111. Q111 2017

     The value of $1+\cot^2\theta$ will be-

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112. Q112 2017

     The value of $\cos\frac{\pi}{3}$ will be-

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113. Q113 2016

     $\sec^2\theta - 1$ is equal to

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114. Q114 2016

     The value of $\sin\frac{\pi}{4}-\cos\frac{\pi}{4}$ will be

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115. Q115 2015

     $\sqrt{2}$ is the value of

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116. Q116 2015

     $9\sec^2\theta - 9\tan^2\theta$ is equal to

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