NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions: Trigonometry has various real-time applications. It is used to solve height and distance problems. This cahpter gives an introduction to basic properties and identities of trigonometric functions and questions based on the same are answered in NCERT solutions for class 11 maths chapter 3 trigonometric functions. You will use the trigonometric identities in other chapters of mathematics and throughout the NCERT physics for both class 11 and 12 also. So it is very important to memorize and understand the basic identities and properties of trigonometric functions. CBSE NCERT solutions for class 11 maths chapter 3 trigonometric functions will help you for the same. Command on this chapter is required to understand the concepts of inverse trigonometric functions which will be taught in class 12. You should practice more in order to get clarity of the concepts. First, try to solve NCERT problems. If you getting difficulties in doing so, you can take help from solutions of NCERT for class 11 maths chapter 3 trigonometric functions. Check all NCERT solutions at a single place which will be helpful when you are not able to solve the NCERT questions. There are four exercises and a miscellaneous exercise in this chapter which are explained below.
Let's understand this chapter with one example.
If we want to measure the height of a building such that we are standing at 50m away from building at point P and the angle of elevation made with the ground at P is 45 degree (as shown in the below figure). Then what will be the height of the building?
Let the height of the building be QR and distance from the base of the building to point P is 50 meter
Using the trigonometric function
There are many other examples such as trigonometry is used in electric circuit analysis, predicting the heights of tides in the ocean, analyzing a musical tone and in seismology, etc.
The main topics of this chapter are listed below:
3.3 Trigonometric Functions
3.4 Trigonometric Functions of Sum and Difference of Two Angles
3.5 Trigonometric Equations
NCERT solutions for class 11 maths chapter 3 trigonometric functions-Exercise: 3.1
CBSE NCERT solutions for class 11 maths chapter 3 trigonometric functions-Exercise: 3.3
Question:1 Prove that
We know the values of sin (30 degree), cos (60 degree) and tan (45 degree). That is:
Question:2 Prove that
The solutions for the given problem is done as follows.
Question:3 Prove that
We know the values of cot(30 degree), tan (30 degree) and cosec (30 degree)
Question:4 Prove that
Using the above values
Question:5(i) Find the value of
We know that
(sin(x+y)=sinxcosy + cosxsiny)
Using this idendity
Question:9 Prove the following
We know that
So, by using these our equation simplifies to
Question:10 Prove the following
Multiply and divide by 2
Now by using identities
-2sinAsinB = cos(A+B) - cos(A-B)
2cosAcosB = cos(A+B) + cos(A-B)
Question:11 Prove the following
We know that
[ cos(A+B) - cos (A-B) = -2sinAsinB ]
By using this identity
Question:13 Prove the following
As we know that
By using these identities
cos2x - cos6x = -2sin(4x)sin(-2x) = 2sin4xsin2x ( sin(-x) = -sin x
cos(-x) = cosx)
cos2x + cos 6x = 2cos4xcos(-2x) = 2cos4xcos2x
So our equation becomes
Question:15 Prove the following
We know that
By using this , we get
sin5x + sin3x = 2sin4xcosx
now nultiply and divide by sin x
Now we know that
By using this our equation becomes
Question:22 prove the following
cot x cot2x - cot3x(cot2x - cotx)
Now we can write cot3x = cot(2x + x)
and we know that
= cotx cot2x - (cot2xcotx -1)
= cotx cot2x - cot2xcotx +1
= 1 = R.H.S.
NCERT solutions for class 11 mathematics
NCERT solutions for class 11- Subject wise
The basic identities used in NCERT solutions for class 11 maths chapter 3 Trigonometric Functions are listed below
The above identities you may have studied in your high school classes also. Here are a few more identities that you have to remember and understand from the NCERT solutions for class 11 maths chapter 3 trigonometric functions
Some conditional identities from the NCERT solutions for class 11 maths chapter 3 Trigonometric Functions
If angles x, y and (x ± y) is not an odd multiple of π 2, then
If angles x, y and (x ± y) is not a multiple of π, then
There are a few more identities used in the NCERT solutions for class 11 maths chapter 3 trigonometric functions which can be derived using the above identities. Try to derive it by your self.
Happy Reading !!!