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RD Sharma's books have been a great companion for the class 12 students preparing for their public examinations. RD Sharma Class 12th FBQ has thirty-five questions in total, having questions like Finding the principal value of trigonometric functions, Measuring angles, Finding the value of x or an expression, and many more. The students who find it hard to solve these questions can use the RD Sharma Class 12 Chapter 3 FBQ Solutions book.

Fill in the blanks The principle value of is ___________.

Principal value cos

Let,

As,

So,

Fill in the blanks The value of is_______.

Principal value of is

now, should be in the given range

is outside the range

As, sin (π – x) = sin x

So,

Fill in the blanks

If cos (tan^{–1}x + cot^{–1} √3) = 0, then value of x is _________.

fill in blanks the set of value of is______________.

Domain of sec

As, is outside domain of sec

Which means there is no set of value of

So, the solution set of is null set or

Fill in the blanks

The principal value of tan^{–1} √3 is _________.

Principal value of tan

Let,

As

so,

The value of

We needd,

Principal value of cos

Also, cos (2nπ + θ) = cos θ for all n ? N

Fill in the blanks

The value of cos (sin^{–1 }x + cos^{–1} x), |x| ≤ 1 is ________.

cos (sin

We know that, (sin

So,

= 0

The value of expression when is___________.

When

We know that, (sin

As, lies in domain

So =

=1

Fill in the blanks if for all x, then ______<y<_____.

We know that,

so

=4 tan

So, y = 4 tan

As, principal value of tan-1 x is

So,

Hence, -2π < y < 2π

The result is true when value of xy is _________.

We have,

Principal range of tan

Let tan

So, A,B

We know that, … (2)

From (1) and (2), we get,

Applying, tan

As, principal range of tan

So, for tan

A-B must lie in – (3)

Now, if both A,B < 0, then A, B

∴ A and -B

So, A – B

So, from (3),

tan

Now, if both A,B > 0, then A, B

∴ A and -B

So, A – B

So, from (3),

tan

Now, if A > 0 and B < 0,

Then, A and B

∴ A and -B

So, A – B (0,π)

But, required condition is A – B

As, here A – B (0,π), so we must have A – B

Applying tan on both sides,

As,

So, tan A < - cot B

Again,

So,

⇒ tan A tan B < -1

As, tan B < 0

xy > -1

Now, if A < 0 and B > 0,

Then, A and B

∴ A and -B

So, A – B (-π,0)

But, required condition is A – B

As, here A – B (0,π), so we must have A – B

Applying tan on both sides,

As,

So, tan B > - cot A

Again,

So,

⇒ tan A tan B > -1

⇒xy > -1

Fill in the blanks

The value of cot^{–1}(–x) for all x ? R in terms of cot^{–1} x is _______.

π – cot

Let cot

⇒ cot A = -x

⇒ -cot A = x

⇒ cot (π – A) = x

⇒ (π – A) = cot

⇒ A = π – cot-1 x

So, cot

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 1

You must know the value of the trigonometric and inverse trigonometric functions.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 2

You must know the value of trigonometric and inverse trigonometric function.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 3

You must know the value of trigonometric and inverse trigonometric function.

Range of

[Inverse trigonometric function]

So, we get

Now, most of us apply the range of as

So, range of

But, we know that domain of is

Hence, term does not hold this value and

So new range becomes,

So, we get

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 4

You must know the rules of trigonometric and inverse trigonometric function.

for some , find the value of .

Inverse trigonometric rule,

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 5

You must know the rules of trigonometric and inverse trigonometric function.

Using the property of inverse trigonometry

Since,=Negative value integer

Using value of inverse trigonometry,

Substituting the value, we get

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 6

You must know the value of inverse trigonometric function.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 7

You must know the value of inverse trigonometric function.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 8

You must know the value of inverse trigonometric function.

, then find

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 9

You must know the rules of inverse trigonometric function.

for all

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 10

You must know the rules of inverse trigonometric function.

, then find

We know

and

Adding both

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 11

You must know the values of inverse trigonometric function.

, then find

Using inverse trigonometry rule,

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 12

You must know the rules of inverse trigonometric function.

, then find

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 13

You must know the rules of inverse trigonometric function.

, then find

Using inverse trigonometric rule,

We know

and

Adding both equations,

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 14

You must know the rules of inverse trigonometric function.

, then find

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 15

You must know the rules of inverse trigonometric function.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 16

You must know the rules of inverse trigonometric function.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 17

You must know the rules of inverse trigonometric function.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 18

You must know the rules of inverse trigonometric function.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 19

You must know the rules of inverse trigonometric function.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 20

You must know the rules of inverse trigonometric function.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 15

You must know the rules of inverse trigonometric function.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 21

You must know the rules of inverse trigonometric function.

, then find

Using inverse rule,

and

Adding both equations,

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 22

You must know the rules of inverse trigonometric function.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 23

**Answer:**

** **_{}

**Hint:**

You must know the sum of three angles of s triangle and inverse trigonometric function.

**Given:**

_{} and _{} are measures of two angles of a triangle, find the third angle.

**Solution:**

Given two angles are_{}and _{}

Let third angle be_{}

** **_{}

_{} _{}

_{}

_{}

_{}

_{}

_{}

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 24

You must know the rules of inverse trigonometric function.

As we know that,

…….. (i)

Substituting the values on equation, we get

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 25

You must know the rules of inverse trigonometric functions

Let

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 26

You must know the rules of inverse trigonometric functions

then

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 27

You must know the rules and values of inverse function

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 28

You must know the rules of inverse functions.

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 29

You must know the rules of inverse function.

Let

Now

So,

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 30

You must know the rules and values of inverse trigonometric functions.

We know,

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 31

You must know the rules of inverse trigonometric function.

Let,

Range of is

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 32

You must know the rules of inverse trigonometric function.

Principal range of is

Let

So must be lie in

Now, if both , then

and

Apply ,

So,

Similarly,

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 33

You must have know about the rules of inverse functions

for all in terms of is

Let

for .

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 34

You must have known about the principal values of inverse functions.

is

Since range of is

Hence, principal value is

Inverse Trigonometric Functions Excercise Fill in the Blanks Question 35

You must have known about the principal values and range of inverse trigonometric function

The range of principal value branch of

Principal value branch of is

And the range is in it is increasing and it is increasing

The function does not have any inflection points

The range of is

Even though the questions are given in objective types, each student must work out the whole sum to find its solution. This consumes time; hence the RD Sharma Class 12 Chapter 3 FBQ solutions will lend a helping hand to the students. Moreover, as the experts deliver the keys, the assurance of the correctness of each answer is strong. And if you belong to the CBSE board institutions, it is a wise option to use the RD Sharma Solutions to increase your ability in solving mathematical solutions.

Moreover, the RD Sharma Class 12th FBQ solutions are available on top educational websites like Career360 for free of cost. Hence, you need not spend hundreds or thousands of rupees in purchasing solution materials. Instead, click on the download button and save the RD Sharma solutions material on your device.

In the RD Sharma Class 12 Solutions Inverse Trigonometry FBQ, there are numerous practice questions that you can try before your tests and exams to increase your efficiency and speed. The students need not search for the answers; it is given in the same order as provided in the textbook. Based on the NCERT pattern, CBSE school students can make the most use of it.

There are many ways to find a solution for a mathematical function. The answers in this book are given in many possible ways. This will make you choose the method that you find easy and prepare accordingly. You can use RD Sharma Class 12th FBQ solutions while doing your homework, making your assignments, and even preparing for the examinations.

Hence, if you start using this book from day 1 in 12th grade, none can stop you from scoring good marks. It is better to make it a practice to work out sums every day from the RD Sharma Class 12 Solutions Chapter 3 FBQ book. Once the students work out the problems from the RD Sharma solution books, they can find themselves with better marks than their previous performance.

There were instances when students had to work out sums from the RD Sharma book during their public exams. Hence, it will be easier to attempt questions from the RD Sharma solutions book if you have practiced. Do not slip the chance of elevating your score by using this free material.

1. How can I increase my speed in solving the FBQs in the Inverse Trigonometry chapter of Class 12?

The Class 12 RD Sharma Chapter 3 FBQ will provide you with straightforward ways of solving the questions most simply. Once you practice via this mode, you will complete this portion quickly during your exams.

2. Where can I find the solutions for Class 12 FBQ online?

You can use the solutions given in the RD Sharma Class 12 Solutions Chapter 3 FBQ available at the Career 360 website. The main advantage is that you need to pay even a single penny to utilize this resource material; everything is available free of cost.

3. What is the best solution guide for the FBQs in Class 12 chapter 3?

Most of the students use the RD Sharma class 12th FBQ solutions book to find accurate answers for the FBQs.

4. Is RD Sharma's book suitable for referring to lengthy solutions or FBQs?

The RD Sharma books are the best guide to search for lengthy solutions and one-word answers. In mathematics, every answer is given on how it has arrived.

5. Which solutions book can the Class 12 students refer to prepare for their public exams?

The RD Sharma solution books are the most recommended materials for students preparing for their class 12 public exams.

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