inverse_trigonometric_lecture_2_part_4
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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)+{\rm 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)