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)