Class 12 Mathematics Important Questions Chapter 2 – Inverse Trigonometric Functions

1 Mark Questions

1. Find the principal value of sin-1 
Ans. Let sin-1



We know that 


There for P.V. of 

2. Find the value of sin-1 
Ans.

When 
= 

3. Find the value of 
Ans.

 

4. Find the value of sin 
Ans.
=1

5. tan-1evaluate
Ans. 

= 

6. Find the principal value of
.
Ans. Let 

7. Find the value of.
Ans. 

Which is principal branch of cos-1x

8. Find the value of 
Ans. 


9. Prove that .

Ans. 

10. Find the principal value of .
Ans. Let 

11. Find the value of.
Ans. 

12. Find the value of 
Ans. 

13. Prove that 
Ans. Put 

13. 
Ans. 

14. Find the principal value of .
Ans. Let 

15. Find the value of.
Ans. 

16. Find the value of 
Ans. 

17. Prove that 
Ans. 

18. 
Ans. Put 

19. Find the principal value of . Ans. Let 

20. Find the value of 
Ans. 

21. Find the value of .
Ans. 

22. Find tan-1 .
Ans. 

23. Find the value of .
Ans. 


4 Marks Questions

1. Find the value of 
Ans. 
As 


=

2. Show that 
Ans. Let 
 





3. Prove that 
Ans. L.H.S =





4. Prove that 
Ans. L.H.S = 

L.H.S = R.H.S

5. Simplify 
Ans. L.H.S = 

L.H.S = R.H.S

6. Explore in the simplest form.
Ans. 



Dividing N and b by 

7. Show that.
Ans.
 


 
 




8. Prove that 
Ans. 


9. Write in simplest form that 
Ans.


10. Prove 
Or Prove that 
Ans.







OR
Put 

11. Prove 
Ans:


12. Simplify.
Ans:

13. Prove that

Ans.Put 





14. If 
Ans. 

15. If a>b>c>0 prove that

Ans.

16. Find the value 
Ans.
Put 

17. Solve.
Ans.

18. Prove that 
Ans.


19. Find the value of 
Ans. Let 



20. If 
Prove that =sin2
Ans. s


Squaring both side

21. If .
Ans. 



22. Show that

Ans. Let 







23. Solve 
Ans. 





24. Find x if .
Ans. 






25. Prove that:

Ans. 




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