NCERT Solutions Class 12

NCERT Solutions Class 12

Inverse Trigonometric Function : NCERT Solutions – Class 12 Maths (Ex 3)

Miscellaneous

Find the value of the following:

1.  

Ans. 

 i.e., , value of  lies in I quadrant.

 = 


2.  

Ans. 

 i.e., , value of  lies in I quadrant.

 = 


3. Prove that:  

Ans. Let   so that 

 

 

Since 

 =  = 

 

 


4. Prove that:  

Ans. Let  so that 

 

 

Again, Let  so that 

 

 

Since 

 

 


5. Prove that:  

Ans. Let  so that 

 

Again, Let  so that 

Since  = 

 

 


6. Prove that:  

Ans. Let  so that 

Again, Let  so that 

 

Since  = 

 

 


7. Prove that:  

Ans. Let  so that 

 

Again, Let  so that 

Since  = 

 

 


8. Prove that:  

Ans. L.H.S. = 

R.H.S.


9. Prove that:  

Ans. Let  so that 

 

 


10. Prove that:  

Ans. We know that   = 

Again,  

L.H.S. = 


11. Prove that:  

Ans. Putting  so that 

L.H.S. = 

Dividing every term by 

 = 

 = R.H.S.


12. Prove that:  

Ans. L.H.S. = 

 …(i) 

Now, let  so that 

From eq. (i),  = R.H.S.


13. Solve the equation:  

Ans. 

 

 

 

 

 


14. Solve the equation:  

Ans. Putting 

 

 

 

 

 


15.  is equal to:

(A)  

(B)  

(C)  

(D) 

Ans. Let  where  so that 

 

Putting 

 

Therefore, option (D) is correct.


16.  then  is equal to:

(A) 

(B)  

(C) 0

(D)  

Ans. Putting  so that 

 

 

 

 

 

  

 

 

  or 

  or 

But  does not satisfy the given equation.

Therefore, option (C) is correct.


 

17.  is equal to:

(A) 

(B) 

(C) 

(D)  

Ans. 

Therefore, option (C) is correct.

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