Derivation of identities for inverse trigo functions part 3

Part - 3 Lecture - 2 Chapter 2 Inverse Trigonometric Functions

 “All progress takes place outside the comfort zone.” –Michael John Bobak

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Summary of this lecture:
Derivation of identities for Inverse Trigonometry Functions

How to study Inverse Trigonometry from my notes and video lectures

Evaluate each of the following:

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

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

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

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

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

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

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

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

35. \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)

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