Inverse Trigonometric Functions

Bihar Board Class 12 · Mathematics · 106 past questions

34 of 106 · show all

1. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $\tan^{-1}\dfrac{x}{y} - \tan^{-1}\dfrac{x-y}{x+y} =$

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2. Q4 2026 Set A2026 Set F

   Prove that $\tan^{-1} 1+\tan^{-1} 2+\tan^{-1} 3=\pi$.

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3. Q5 2026 Set A2026 Set H2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   Find the value of $2\tan^{-1}\frac{1}{3}+\tan^{-1}\frac{1}{7}$.

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4. Q6 2026 Set A

   Prove that $\sec^2(\tan^{-1} 2)+\operatorname{cosec}^2(\cot^{-1} 3)=15$.

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5. Q7 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $\tan^{-1}2 + \tan^{-1}3 =$

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6. Q11 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   If $|x| \le 1$, then $\tan(\cos^{-1}x) =$

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7. Q15 2026 Set E

   Find the value of $2\tan^{-1}\frac13+\tan^{-1}\frac17$.

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8. Q17 2026 Set F2026 Set B2026 Set D

   $\cos^{-1}(\cos\frac{7\pi}{6}) =$

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9. Q20 2026 Set H2026 Set E2026 Set C2026 Set B2026 Set F2026 Set J2026 Set D2019 Set F

   Prove that $\sec^2(\tan^{-1}2) + \operatorname{cosec}^2(\cot^{-1}3) = 15$

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10. Q21 2026 Set H2026 Set E2026 Set C2026 Set D2026 Set J2026 Set B

    Prove that $\tan^{-1}1+\tan^{-1}2+\tan^{-1}3=\pi$.

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11. Q23 2026 Set H

    $\tan^{-1}(1)+\cos^{-1}\left(-\frac12\right)+\sin^{-1}\left(-\frac12\right) =$

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12. Q30 2025

    $\sin\left[\dfrac{\pi}{3} - \sin^{-1}\left(\dfrac{-1}{2}\right)\right] =$

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13. Q31 2025

    $\sin(\tan^{-1}x) =$, $|x| < 1$

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14. Q32 2025

    $\sin^{-1}\sin\left(\dfrac{3\pi}{5}\right) =$

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15. Q35 2025

    If $\cos^{-1}\alpha + \cos^{-1}\beta + \cos^{-1}\gamma = 3\pi$, then find the value of…

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16. Q36 2025

    Solve the equation $\cos(\tan^{-1}x) = \sin\left(\cot^{-1}\frac{3}{4}\right)$.

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17. Q37 2025

    Prove that $\sin^{-1}\frac{5}{13} + \cos^{-1}\frac{3}{5} = \tan^{-1}\frac{63}{16}$.

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18. Q38 2025 Set A2025 Set E

    $\cot^{-1}\left(\tan\dfrac{\pi}{7}\right) =$

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19. Q41 2025 Set A2025 Set E

    $\cos^{-1}x+\sec^{-1}\frac{1}{x}=$

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20. Q43 2025 Set A2025 Set E

    $\sin\left\{\sin^{-1}\frac{1}{5}+\cos^{-1}x\right\}=1,\ \Rightarrow x=$

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21. Q48 2024 Set D2024 Set J

    $\sin(\cot^{-1}x)=$

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22. Q49 2024 Set D2024 Set J

    Prove that $4(\cot^{-1}3+\cot^{-1}2)=\pi$.

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23. Q53 2024 Set D2024 Set J

    $\tan^{-1}\sqrt{3} - \sec^{-1}(-2) =$

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24. Q60 2023

    $\sin^{-1}\left(\sin\dfrac{2\pi}{3}\right) =$

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25. Q73 2021 Set I

    $2\tan^{-1}\dfrac13+\tan^{-1}\dfrac17 =$

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26. Q77 2021 Set J2021 Set I2018

    Prove that…

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27. Q80 2021 Set J2021 Set I

    $3\sin^{-1}x = \ldots\ldots\ldots\ldots,\ |x|\le\dfrac12$

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28. Q86 2021 Set J

    $2\tan^{-1}\frac{1}{3} + \tan^{-1}\frac{1}{7} =$

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29. Q91 2018

    $\cos^{-1}(2x-1) =$

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30. Q92 2018

    $2\cot^{-1}3+\cos^{-1}7=$

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31. Q94 2018

    Prove that $\sin^{-1}\frac{3}{5}-\cos^{-1}\frac{12}{13}=\sin^{-1}\frac{16}{65}$

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32. Q96 2017

    $\tan^{-1}\frac{1}{2} + \tan^{-1}\frac{1}{4} = \ldots\ldots\ldots\ldots$

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33. Q102 2016

    Solve for x: $\tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}$

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34. Q106 2015

    Prove that $4\left(\cot^{-1}3+\operatorname{cosec}^{-1}\sqrt{5}\right)=\pi$

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