Ch02. Inverse Trigonometric Functions

In this self study course, you will learn definition, range, domain, principal value branch, graphs of inverse trigonometric functions and elementary properties of inverse trigonometric functions. For further understanding of concepts and for examination preparation, practice questions based on the above topics are discussed in the form of assignments that have questions from NCERT Textbook exercise, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

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10 hours 55 minutes Course Duration
English Syllabus medium
Hindi + English Explanation
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✍ Practice Time – 3

It's time for you to practice the questions that I have discussed.

Instructions:

  • You might watch the practice video in case you need any help or instructions to continue with the practice.

Evaluate each of the following:

15. {\displaystyle \tan \left[\frac{1}{2} \cos ^{-1} \left(\frac{2}{\sqrt{5} } \right)\right ]}

21. { \displaystyle \sin ^{-1} \left(-\frac{\sqrt{3} }{2} \right)+\cos ^{-1} \left(-\frac{1}{2} \right)+\tan ^{-1} \left(-\frac{1}{\sqrt{3} } \right)}

22. { \displaystyle \tan ^{2} (sec ^{-1} 2)+cot ^{2} (\cosec^{-1} 3)}

23. { \displaystyle \sin \left(2\tan ^{-1} \frac{1}{3} \right)+\cos (\tan ^{-1} 2\sqrt{2} )}

25. { \displaystyle \sin (\tan ^{-1} x+cot ^{-1} x)}

26. { \displaystyle \sin \left(\cos ^{-1} \frac{4}{5} \right)}

27. { \displaystyle \sin \left(cot ^{-1} \frac{4}{3} \right)}

28. { \displaystyle \sin (cot ^{-1} x)}

35. { \displaystyle \tan \frac{1}{2} \left[\sin ^{-1} \frac{2x}{1+x^{2} } +\cos ^{-1} \frac{1-y^{2} }{1+y^{2} } \right ], |x|<1, y>0, \text{ and }, xy<1} (NCERT Exercise 2.2 Q13)

19. { \displaystyle \tan \left \{ 2\tan ^{-1} \frac{1}{5} -\frac{\pi }{4} \right \} }

20. { \displaystyle \sin ^{-1} \left(\cos \left(\frac{43\pi }{5} \right)\right)}

24. { \displaystyle \sec ^{2} (\tan ^{-1} 2)+{\csc}^{2} (cot ^{-1} 3)}

29. { \displaystyle \cos (\tan ^{-1} x)}

30. { \displaystyle \sin ^{-1} \frac{1}{2} -2\sin ^{-1} \frac{1}{\sqrt{2} } }

31. { \displaystyle \tan \left(\cos ^{-1} \frac{4}{5} +\tan ^{-1} \frac{2}{3} \right)} (NCERT Exercise 2.2 Q18)

32. { \displaystyle \tan \left(2\tan ^{-1} \frac{1}{5} \right)}

33. { \displaystyle \tan \left[2\cos \left(2\sin ^{-1} \frac{1}{2} \right)\right ]} (NCERT Exercise 2.2 Q11)

34. { \displaystyle cot (\tan ^{-1} a+cot ^{-1} a)} (NCERT Exercise 2.2 Q12)

36. { \displaystyle \sin (\tan ^{-1} x) , |x|<1} (NCERT Miscellaneous Exercise Q15)

37. { \displaystyle \tan ^{-1} \left(\frac{x}{y} \right)-\tan ^{-1} \left(\frac{x-y}{x+y} \right)} (NCERT Miscellaneous Exercise Q17)

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