  #### Need solution for RD Sharma maths Class 12 Chapter Inverse Trignometric Function Exercise 3.3 Question 3 Sub question (i) maths text book solution. Hint : The branch with range is called the principal value branch of function .

Thus,

The branch with range is called the principal value branch of the function .

Thus,

The branch with range is called the principal value branch.

Thus,

Domain of functions and are and respectively.

Given :

Explanation :

Let us first solve for

Let

...(i)

[From equation (i)]

Range of principal value branch of is

Therefore principal of value of is                                                         ....(ii)

Now,

Let us solve for

Let                                                                                        ....(iii)

[From equation (iii)]

The range of principal value branch of is .

Principal value of                                                              ......(iv)

Now,

Let us solve for

Let                                                                                              ....(v)

[From equation (v)]

The range of principal value branch of is .

Principal value of is                                                                     ...(vi)

Now,

Putting the values from equations (ii), (iv) and (vi)

#### infoexpert23 