Inverse Trigonometric Functions

Bihar Board Class 12 · Mathematics · 106 past questions

25 of 106 · show all

1. Q1 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $x \in R$, $\cot(\tan^{-1}x + \cot^{-1}x) =$

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

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

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3. Q3 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $|x| \le 1$, $\cos^{-1}\left(\dfrac{1-x^2}{1+x^2}\right) =$

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4. Q4 2026 Set A2026 Set F

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

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

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

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6. Q6 2026 Set A

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

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

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

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8. Q8 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I

   $\tan^{-1}\left(-\dfrac{1}{\sqrt{3}}\right) =$

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9. Q9 2026 Set A2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

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

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10. Q10 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set J2024 Set J2024 Set D

    $\cos^{-1}\left(\cos\dfrac{7\pi}{6}\right) =$

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

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

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12. Q12 2026 Set B2026 Set D

    $\tan^{-1}(1) + \cos^{-1}(-\frac{1}{2}) + \sin^{-1}(-\frac{1}{2}) =$

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13. Q13 2026 Set C

    $\frac{d}{dx}(\tan^{-1}\sqrt{x} + \cot^{-1}\sqrt{x}) =$

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14. Q14 2026 Set C

    $\frac{d}{dx}(2\tan^{-1}x) =$

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15. Q15 2026 Set E

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

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16. Q16 2026 Set E2026 Set C2026 Set D

    $\sin(\cos^{-1}\frac{3}{5}) =$

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17. Q17 2026 Set F2026 Set B2026 Set D

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

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18. Q18 2026 Set F

    $\sin(\cos^{-1} 3/5) =$

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19. Q19 2026 Set F

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

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

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

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

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

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22. Q22 2026 Set H

    $2\tan^{-1}\frac13 =$

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23. Q23 2026 Set H

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

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24. Q24 2026 Set J2026 Set A2026 Set B2026 Set H

    $\sin(\cos^{-1}3/5) =$

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25. Q25 2026 Set J2026 Set A2026 Set C2026 Set E

    $\tan^{-1}(1) + \cos^{-1}\left(-\dfrac{1}{2}\right) + \sin^{-1}\left(-\dfrac{1}{2}\right)$

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