# Class 12 NCERT Solutions- Mathematics Part I – Chapter 2 Inverse Trigonometric Functions – Miscellaneous Exercise on Chapter 2 | Set 1

### Question 1. Find the value of

Solution:

We know that

Here,

Now,  can be written as :

, where

Hence, the value of  = Ï€/6

### Question 2. Find the value of

Solution:

We know that

Here,

Now,  can be written as:

where

Hence, the value of  = Ï€/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

Solution:

L.H.S.

–

= Ï€/4

L.H.S = R.H.S

Hence proved

Solution:

Let x = tan2Î¸

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

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