Course Content

Expand All
Topic Content
0% Complete 0/5 Steps
Topic Content
0% Complete 0/1 Steps
Topic Content
0% Complete 0/1 Steps

✍ 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)

Topic Content
0% Complete 0/17 Steps
Topic Content
0% Complete 0/19 Steps
Topic Content
0% Complete 0/14 Steps