HOTS questions inverse trigonometry lecture 2 part 4

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Part - 4 Lecture - 2 Chapter 2 Inverse Trigonometric Functions

“You may only succeed if you desire succeeding; you may only fail if you do not mind failing.” –Philippos

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Evaluate each of the following:

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

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

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

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

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

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

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

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

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

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

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

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