NCERT Solutions Class 12 Maths (Inverse Trigonometric Functions) Miscellaneous Exercise

NCERT Solutions Class 12 Maths from class 12th Students will get the answers of Chapter-2 (Inverse Trigonometric Functions) Miscellaneous Exercise This chapter will help you to learn the basics and you should expect at least one question in your exam from this chapter.
We have given the answers of all the questions of NCERT Board Mathematics Textbook in very easy language, which will be very easy for the students to understand and remember so that you can pass with good marks in your examination.

Set-1

Question 1. Find the value of 

Solution: 

We know that  

Here, 

Now,  can be written as :

, where 

Hence, the value of  = π/6

Question 2. Find the value of 

Solution: 

We know that 

Here, 

Now,  can be written as:

      

 where 

Hence, the value of  = π/6

Question 3. Prove 

Solution: 

Let           -(1)

sin x = 3/5

So,= 4/5

tan x = 3/4

Hence, 

Now put the value of x from eq(1), we get

Now, we have

L.H.S 

=                 –

Hence, proved.

Question 4. Prove 

Solution: 

Let  

Then sin x = 8/17 

 cos x = = 15/17

Therefore, 

         -(1)

Now, let 

Then, sin y = 3/5 

 = 4/5

     -(2)

Now, we have:

L.H.S.

 From equation(1) and (2), we get

=                          

= 

=                                  –

= 

Hence proved

Question 5. Prove 

Solution: 

Let 

Then, cos x = 4/5

 = 3/5

        -(1)

Now let 

Then, cos y = 3/4 

            -(2)

Let  

Then, cos z = 33/65

sin z = 56/65 

    -(3)

Now, we will prove that : 

L.H.S. 

From equation (1) and equation (2)

=                                                                  

=          –

= 

= 

Using equation(3)

=                                                                                                   

Hence proved

Question 6. Prove  

Solution: 

Let   

Then, sin x = 3/5 

 = 4/5

           -(1)

Now, let   

Then, cos y = 12/13 and sin y = 5/13

        -(2)                                                             

Let 

Then, sin z = 56/65 and cos z = 33/65

           -(3)

Now, we have:

L.H.S.=

From equation(1) and equation(2)

=                                                                           

=                –

= 

= 

From equation (3)

=     

Hence proved                                                                                                           

Question 7. Prove  

Solution: 

Let    

Then, sin x = 5/13 and cos x = 12/13.

                   -(1)

Let      

Then, cos y = 3/5 and sin y = 4/5

                -(2)

From equation(1) and (2), we have

R.H.S.

=

=           –

=

=

L.H.S = R.H.S

Hence proved

Question 8. Prove 

Solution: 

L.H.S.

=      –

= 

= 

= 

= 

= 

= 

= π/4 

L.H.S = R.H.S

Hence proved

Question 9. Prove 

Solution: 

Let x = tan2θ

Then,

Now, we have

R.H.S = 

L.H.S = R.H.S

Hence proved

Question 10. Prove 

Solution: 

Consider

By rationalizing

=                         

=

=

= 

L.H.S = = x/2

L.H.S = R.H.S

Hence proved

Set-2

Question 11. Prove 

Solution: 

Put  so that, 

Then, we have :

LHS = 

= 

= 

= 

= 

      – 

  

L.H.S = R.H.S

Hence Proved

Question 12. Prove 

Solution: 

L.H.S. = 

= 

Using 

=       -(1)

Now, let  Then, 

 

Using equation(1), we get,

= 

L.H.S = R.H.S

Hence Proved

Question 13. Solve 

Solution:

=                      –

= 

= 

= cos x/sin x

= cot x =1

Therefore, x = π/4​

Question 14. Solve 

Solution:

Let x = tanθ

        

π/4 – θ = θ/2

θ = π/6

So, x = tan(π/6) = 1/√3

Question 15. Solve  is equal to
(A)     (B)  (C) (D) 

Solution:

Let tan y = x, 

Let  Then,

So, the correct answer is D.

Question 16. Solve , then x is equal to
(A) 0, 1/2      (B) 1, 1/2      (C) 0     (D) 1/2 

Solution:

        -(1)

Let 

Therefore, from equation(1), we have

Put x = siny then, we have:

sin y = 0 or 1/2

x = 0 or x = 1/2

But, when x = 1/2 it can be observed that:

L.H.S. = 

= 

= 

= 

x = 1/2 is not the solution of given equation.

Thus, x = 0 

Hence, the correct answer is C

Question 17. Solve  is equal to

(A) π​/2      (B) π​/3     (C) π​/4      (D) -3π​/4  

Solution:

                –

Hence, the correct answer is C