Introduction to Trigonometry

CBSE Class 10 · Mathematics · 60 past questions

These are the board's own papers. 130 more board questions reprinted in the books we use in class are for signed-in students: sign in.

1. Q1 2026

   Given that $\sin 2\alpha = \frac{\sqrt{3}}{2}$, the value of $\sin 3\alpha$ is…

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2. Q2 2026

   The value of $\left(\frac{1}{2}\tan^2 45^\circ - \cos^2 60^\circ\right)$ is…

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3. Q3 2026

   For an acute angle $\theta$, if $\sin\theta=\frac{1}{9}$, then value of…

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4. Q4 2026

   Simplest form of $\frac{\sec A}{\sqrt{\sec^2A-1}}$ is

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5. Q5 2026

   Evaluate : $\frac{\sin^3 60^\circ - \tan 30^\circ}{\cos^2 45^\circ}$

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6. Q6 2026

   Prove that…

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7. Q7 2026

   When $\sin A=\frac{1}{3}$, the value of $\cot A$ is

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8. Q8 2026

   $\frac{1+\tan^2 A}{1+\cot^2 A}$ equals to…

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9. Q9 2026

   Prove that : $\sqrt{\dfrac{1+\sin A}{1-\sin A}} = \sec A + \tan A$

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10. Q10 2026

    Prove that : $\frac{\sin\theta-\cos\theta+1}{\sin\theta+\cos\theta-1}=\frac{1}{\sec\theta-\tan\theta}$

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11. Q11 2026 (Basic)

    The value of $\sin 90^\circ \cos 90^\circ - \sin^2 60^\circ$ is…

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12. Q12 2026 (Basic)

    If $\sin\theta=\frac{1}{7}$, then $\tan\theta$ is…

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13. Q13 2026 (Basic)

    If $\sin(A - B) = \frac{1}{2}$ and $\tan(A + B) = \sqrt{3}$, $0° \le A + B < 90°$, $A > B$ then find the…

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14. Q14 2026 (Basic)

    Prove that $\frac{\cot A - \cos A}{\cot A + \cos A} = \frac{\sec A - \tan A}{\sec A + \tan A}$

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15. Q15 Sample paper 2026-27

    If $\tan (A + B) = \sqrt{3}$ and $\tan (A - B) = \frac{1}{\sqrt{3}}$, $0° < A + B < 90°$, $A > B$, then the…

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16. Q16 Sample paper 2026-27

    If $\tan\theta = \frac{1}{\sqrt{5}}$, then find the value of…

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17. Q17 Sample paper 2026-27

    During a math class, Ms. Isha wrote the expression given below on the board and asked the students to…

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18. Q18 2025

    If $7\cos^2\theta + 3\sin^2\theta = 4$, then the value of $\theta$ is…

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19. Q19 2025

    If $\sin 30^\circ \tan 45^\circ = \frac{\sec 60^\circ}{k}$, then the value of k is…

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20. Q20 2025

    If $\tan A = \sqrt{3}$; where A is an acute angle, then find the value of $\frac{\sin^2 A}{1 + \cos^2 A}$.

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21. Q21 2025

    Prove that…

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22. Q22 2025

    If $\tan 3\theta = \sqrt{3}$, then $\frac{\theta}{2}$ equals…

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23. Q23 2025

    (cot θ + tan θ) equals…

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24. Q24 2025

    If $4k = \tan^2 60^\circ - 2\operatorname{cosec}^2 30^\circ - 2\tan^2 30^\circ$, then find the value of k.

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25. Q25 2025

    Prove that: $\sqrt{\frac{\sec A-1}{\sec A+1}}+\sqrt{\frac{\sec A+1}{\sec A-1}}=2\operatorname{cosec}A$

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26. Q26 2025

    If $\theta$ is an acute angle and $7 + 4\sin\theta = 9$, then the value of $\theta$ is…

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27. Q27 2025

    The value of $\tan^2\theta - \left(\frac{1}{\cos\theta} \times \sec\theta\right)$ is…

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28. Q28 2025

    If $x\cos 60^\circ + y\cos 0^\circ + \sin 30^\circ - \cot 45^\circ = 5$, then find the value of $x + 2y$.

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29. Q29 2025

    Prove that…

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30. Q30 2025 (Basic)

    Which of the following statements is *false* ?

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31. Q31 2025 (Basic)

    The value of $\left(\tan^2 A - \frac{1}{\cos^2 A}\right)$ is…

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32. Q32 2025 (Basic)

    Prove that…

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33. Q33 2025 (Basic)

    An injured bird was found on the roof of a building. The building is 15 m high. A fireman was called to… (with a figure)

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34. Q34 2024

    If $\cos\theta = \frac{\sqrt{3}}{2}$ and $\sin\phi = \frac{1}{2}$, then $\tan(\theta + \phi)$ is…

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35. Q35 2024

    Evaluate : $\frac{\cos 45° + \sin 60°}{\sec 30° + \operatorname{cosec} 30°}$.

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36. Q36 2024

    Prove that $\frac{\sin\theta - 2\sin^3\theta}{2\cos^3\theta - \cos\theta} = \tan\theta$.

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37. Q37 2024

    If $\sin\theta = \cos\theta$, $(0° < \theta < 90°)$, then value of $(\sec\theta \cdot \sin\theta)$ is…

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38. Q38 2024

    Evaluate : $2\sin^2 30^\circ \sec 60^\circ + \tan^2 60^\circ$.

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39. Q39 2024

    Prove that $\frac{1+\sec\theta-\tan\theta}{1+\sec\theta+\tan\theta}=\frac{1-\sin\theta}{\cos\theta}$.

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40. Q40 2024

    If $\sec\theta - \tan\theta = m$, then the value of $\sec\theta + \tan\theta$ is…

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41. Q41 2024

    If $\cos(\alpha + \beta) = 0$, then value of $\cos\left(\frac{\alpha + \beta}{2}\right)$ is equal to…

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42. Q42 2024

    Evaluate : $2\sqrt{2}\cos 45^{\circ}\sin 30^{\circ} + 2\sqrt{3}\cos 30^{\circ}$

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43. Q43 2024

    Prove that : tanθ/(1-cotθ) + cotθ/(1-tanθ) = 1 + secθ cosecθ

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44. Q44 2024 (Basic)

    If $\sin\theta = \frac{1}{3}$, then $\sec\theta$ is equal to…

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45. Q45 2024 (Basic)

    For what value of $\theta$, $\sin^2\theta + \sin\theta + \cos^2\theta$ is equal to 2 ?

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46. Q46 2024 (Basic)

    Evaluate: $\sin A \cos B + \cos A \sin B$; if $A = 30°$ and $B = 45°$.

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47. Q47 2024 (Basic)

    Prove that : $(\cot\theta-\operatorname{cosec}\theta)^2=\dfrac{1-\cos\theta}{1+\cos\theta}$.

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48. Q48 2023

    If $4\cot^2 45^\circ - \sec^2 60^\circ + \sin^2 60^\circ + p = \frac{3}{4}$, then find the value of p.

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49. Q49 2023

    Prove that…

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50. Q50 2023

    If a pole 6 m high casts a shadow $2\sqrt{3}$ m long on the ground, then sun's elevation is…

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51. Q51 2023

    $\sec\theta$ when expressed in terms of $\cot\theta$, is equal to…

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52. Q52 2023

    Evaluate $\frac{5\cos^2 60^\circ + 4\sec^2 30^\circ - \tan^2 45^\circ}{\sin^2 30^\circ + \cos^2 30^\circ}$

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53. Q53 2023

    Prove that $\frac{\sin A - 2\sin^3 A}{2\cos^3 A - \cos A} = \tan A$

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54. Q54 2023

    If $2 \tan A = 3$, then the value of $\frac{4 \sin A + 3 \cos A}{4 \sin A - 3 \cos A}$ is

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55. Q55 2023

    $\left[\frac{3}{4}\tan^2 30° - \sec^2 45° + \sin^2 60°\right]$ is equal to

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56. Q56 2023

    If $\sin\theta + \cos\theta = \sqrt{3}$, then find the value of $\sin\theta \cdot \cos\theta$.

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57. Q57 2023

    Prove that : $\frac{\tan\theta+\sec\theta-1}{\tan\theta-\sec\theta+1}=\frac{1+\sin\theta}{\cos\theta}$

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58. Q58 2023 (Basic)

    If $2\cos\theta = 1$, then the value of $\theta$ is

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59. Q59 2023 (Basic)

    Evaluate : $\tan^2 60^\circ - 2\,\text{cosec}^2 30^\circ - 2\tan^2 30^\circ$.

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60. Q60 2023 (Basic)

    Prove that…

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