OP Malhotra Inverse Trigonometry Function S.Chand ISC Class-12 Maths Solutions Ch-4. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-4, Self Revision, Similar Questions for Practice and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## OP Malhotra Inverse Trigonometry Function S.Chand ISC Class-12 Maths Solutions Ch-4

Class: | 12th |

Subject: | Mathematics |

Chapter : | Ch-4 Inverse Trigonometry Function of Section -A |

Board | ISC |

Writer | OP Malhotra, SK Gupta, Anubhuti Gangal |

Publications | S.Chand Publications 2020-21 |

**-: Included Topics :- **

Exe-4

Self Revision

Chapter Test

Similar Questions for Practice

### OP Malhotra Inverse Trigonometry Function S.Chand ISC Class-12 Maths Solutions Ch-4

**Inverse Trigonometric Functions:**

Trigonometric functions are many-one functions but we know that inverse of function exists if the function is bijective. If we restrict the domain of trigonometric functions, then these functions become bijective and the inverse of trigonometric functions are defined within the restricted domain. The inverse of f is denoted by ‘f^{-1.}

**or**

The inverse trigonometric functions are also known as** arc function** as they produce the length of the arc, which is required to obtain that particular value. There are six inverse trigonometric functions which include arcsine (sin^{-1}), arccosine (cos^{-1}), arctangent (tan^{-1}), arcsecant (sec^{-1}), arccosecant (cosec^{-1}), and arccotangent (cot^{-1}).

**Inverse Rational Function :**

A rational function is a function of form f(x) = P(x)/Q(x) where Q(x) ≠ 0. To find the inverse of a rational function, follow the following steps. An example is also given below which can help you to understand the concept better.

**Step 1:**Replace f(x) = y**Step 2:**Interchange x and y**Step 3:**Solve for y in terms of x**Step 4:**Replace y with f^{-1}(x) and the inverse of the function is obtained.

**Exe-4**

OP Malhotra Inverse Trigonometry Function S.Chand ISC Class-12 Maths Solutions Ch-4

Question 1:

Write down the value of :

(i)…………….

……………….

Question 2:

Find :

(i) cos A …………

…………………………

Question 3:

……………….

………………..

………………

Question 30:

If cos-¹ x + cos-¹ y + cos-¹z = π prove that ……………….

**Inverse Function :**

If y = f(x) and x = g(y) are two functions such that f (g(y)) = y and g (f(y)) = x, then f and y are said to be inverse of each other

i.e., g = f^{-1}

IF y = f(x), then x = f^{-1}(y)

^{-1}(y) will return the value x.

**Self Revision**

OP Malhotra Inverse Trigonometry Function S.Chand ISC Class-12 Maths Solutions Ch-4

Question 1:

Prove that :

……………………

Question 2:

Solve the equation

tan………………..

Question 3:

Show that sin ………………….

Question 4:

……………………

……………………

……………………

Question 24:

If sin-¹x + tan-¹x = x/2 prove that ……………..

**Inverse Trigonometric Functions :**

If y = sin X^{-1}, then x = sin^{-1} y, similarly for other trigonometric functions.

This is called inverse trigonometric function .

Now, y = sin^{-1}(x), y ∈ [π / 2 , π / 2] and x ∈ [-1,1].

(i) Thus, sin^{-1}x has infinitely many values for given x ∈ [-1, 1].

(ii) There is only one value among these values which lies in the interval [π / 2 , π / 2]. This value is called the principal value.

**Chapter Test**

### OP Malhotra Inverse Trigonometry Function S.Chand ISC Class-12 Maths Solutions Ch-4

Question 1:

Find the principal value of ……….

(i)………….

………………..

Question 2:

Find the value of

(i) sin ………………..

(ii) cot ………….

Question 3:

Prove that

…………………

Question 4:

…………………….

……………………

……………………

Question 18:

2tan-¹ (1/2) + tan-¹(1/7) = sin-¹……….

**Inverse Hyperbolic Functions :**

Just like inverse trigonometric functions, the inverse hyperbolic functions are the inverses of the hyperbolic functions. There are mainly 6 inverse hyperbolic functions exist which include sinh^{-1}, cosh^{-1}, tanh^{-1}, csch^{-1}, coth^{-1}, and sech^{-1}. Check out inverse hyperbolic functions formula to learn more about these functions in detail.

-: End of Inverse Trigonometry Function **OP Malhotra S. Chand **ISC Class-12 Maths Chapter-4 Solution :-

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