NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

By Mr Ahmad

Published on:

Follow Us

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8

NCERT Solutions For Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8 are prepared by specialised experienced mathematic teacher. Maths are most important subject of board and with the help of this chapter-wise NCERT solution and little practices you can get very good marks in your respective board exam. It also help to build a foundation for topics that will be covered in the upcoming 11th and 12th. Student can also check the Important Question with solution for class 9 to class 12.

Also Check – Best laptop under 30000 for student

Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8 contain total 4 exercise that has 27 questions and it covered the topic trigonometric ratios of the angles, trigonometric ratios for angles of 00 and 900 , trigonometric ratios of complementary angles.  Check Previous chapter – NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry.

Important Formula

Trigonometric Ratios of Complementary Angles

sin (90° – A) = cos A,

cos (90° – A) = sin A,

tan (90° – A) = cot A,

cot (90° – A) = tan A,

sec (90° – A) = cosec A,

cosec (90° – A) = sec A

sin2 A + cos2 A = 1,

sec2 A – tan2 A = 1 for 0° ≤ A < 90°,

cosec2 A = 1 + cot2 A for 0° < A ≤ 90°

Trigonometry Table

Angle30°45°60°90°
Sinθ01/21/√2√3/21
Cosθ1√3/21/√2½0
Tanθ01/√31√3Not defined
CotθNot defined√311/√30
Secθ12/√3√22Not defined
CosecθNot defined2√22/√31

Trigonometric Ratios

Trigonometric ratios of an acute angle in a right triangle express the relationship between the angle and the length of its sides.
Let ∆ABC be a triangle right angled at B. Then the trigonometric ratios of the angle A in right ∆ABC are defined as follows:
NCERT Solutions For Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.1 Q11

NCERT Solutions For Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.1 Q11.1

Exercise 8.1

Question 1.
In ∆ABC right angled at B, AB = 24 cm, BC = 7 cm. Determine:
(i) sin A, cos A
(ii) sin C, cos C
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.1 Q1

Question 2.
In given figure, find tan P – cot R.
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.1 PDF Download Q2

 

Question 3.
If sin A = 3/4, Calculate cos A and tan A
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.1 PDF Q3

Question 4.
Given 15 cot A = 8, find sin A and sec A.
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.1 Free PDF Download Q4

Question 5.
Given sec θ = 13/12 Calculate all other trigonometric ratios
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.1 Q5

Question 6.
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
Solution:
Exercise 8.1 Class 10 NCERT Solutions Chapter 8 Trigonometry Q6

Question 7.
If cot θ = 78, evaluate:
(i) (1+𝑠𝑖𝑛𝜃)(1𝑠𝑖𝑛𝜃)(1+𝑐𝑜𝑠𝜃)(1𝑐𝑜𝑠𝜃)
(ii) cot²θ
Solution:
Exercise 8.1 Class 10 NCERT Solutions Chapter 8 Trigonometry Free PDF Download Q7

Question 8.
If 3 cot A = 4, check whether 1𝑡𝑎𝑛2𝐴1+𝑡𝑎𝑛2𝐴 = cos² A – sin² A or not.
Solution:
Exercise 8.1 Class 10 NCERT Solutions Chapter 8 Trigonometry Free PDF Download Q7

Question 9.
In triangle ABC, right angled at B, if tan A = 13, find the value of:
(i) sin A cos C + cos A sin C
(ii) cos A cos C – sin A sin C
Solution:
Trigonometry Class 10 Chapter 8 Exercise 8.1 NCERT Solutions Free PDF Download Q9
Trigonometry Class 10 Chapter 8 Exercise 8.1 NCERT Solutions PDF Q9.1

Question 10.
In ΔPQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
Solution:
Trigonometry Class 10 Chapter 8 Exercise 8.1 NCERT Solutions Q10

Question 11.
State whether the following statements are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) sec A = 125 for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin θ = 43 for some angle.
Solution:
Trigonometry Class 10 Chapter 8 Exercise 8.1 NCERT Solutions PDF Download Q11

Exercise 8.2

1. Evaluate the following:

(i) sin 60° cos 30° + sin 30° cos 60°

(ii) 2 tan2 45° + cos2 30° – sin2 60

Ncert solutions class 10 chapter 8-4

Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.2 Free PDF Download Q1
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.2 PDF Download Q1.1

Question 2.
Choose the correct option and justify your choice:
NCERT Solutions For Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 Q2
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.2 Q2

Question 3.
If tan (A + B) = √3 and tan (A – B) = 13; 0° < A + B ≤ 90°; A > B, find A and B.
Solution:
Exercise 8.2 Class 10 NCERT Solutions Chapter 8 Trigonometry PDF Download Q3

Question 4.
State whether the following statements are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin θ increases as θ increases.
(iii) The value of cos θ increases as θ increases.
(iv) sin θ = cos θ for all values of θ.
(v) cot A is not defined for A = 0°.
Solution:
Trigonometry Class 10 Chapter 8 Exercise 8.2 NCERT Solutions Q4

Exercise 8.3

Question 1.
Evaluate:
NCERT Solutions For Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 Q1
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.3 Free PDF Download

Question 2.

(i) tan 48° tan 23° tan 42° tan 67° = 1

(ii) cos 38° cos 52° – sin 38° sin 52° = 0

Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.3 Free PDF Q2

Question 3.
If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.3 Q3

Question 4.
If tan A = cot B, prove that A + B = 90°.
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.3 PDF Q4

Question 5.
If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.
Solution:
Exercise 8.3 Class 10 NCERT Solutions Chapter 8 Trigonometry PDF Download Q5

Question 6.
If A, B and C are interior angles of a triangle ABC, then show that: sin (𝐵+𝐶2) = cos 𝐴2
Solution:
Exercise 8.3 Class 10 NCERT Solutions Chapter 8 Trigonometry PDF Q6

Question 7.
Express sin 61° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.
Solution:
Trigonometry Class 10 Chapter 8 Exercise 8.3 NCERT Solutions Q7

Exercise 8.4

Question 1.

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

Solution:

NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.4 Free PDF Download Q1

 

Question 2.
Write all the other trigonometric ratios of ∠A in terms of sec A.
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.4 Q2

Question 3.
Evaluate:
NCERT Solutions For Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4 Q3
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.4 Free PDF Q3

Question 4.

Choose the correct option. Justify your choice.
(i) 9 sec2A – 9 tan2A =
(A) 1                 (B) 9              (C) 8                (D) 0
(ii) (1 + tan θ + sec θ) (1 + cot θ – cosec θ)
(A) 0                 (B) 1              (C) 2                (D) – 1
(iii) (sec A + tan A) (1 – sin A) =
(A) sec A           (B) sin A        (C) cosec A      (D) cos A

(iv) 1+tan2A/1+cot2A = 

      (A) sec2 A                 (B) -1              (C) cot2A                (D) tan2A

 

Solution:
Exercise 8.4 Class 10 NCERT Solutions Chapter 8 Trigonometry PDF Download Q4

Question 5.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
NCERT Solutions For Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4 Q5
Solution:
Exercise 8.4 Class 10 NCERT Solutions Chapter 8 Trigonometry Free PDF Download Q4
Trigonometry Class 10 Chapter 8 Exercise 8.4 Free PDF Download Q5.1
Trigonometry Class 10 Chapter 8 Exercise 8.4 NCERT Solutions Q5.2
Exercise 8.4 Class 10 NCERT Solutions Chapter 8 Trigonometry Q5.3
Exercise 8.4 Class 10 NCERT Solutions Chapter 8 Trigonometry PDF Q5.4
NCERT Solutions for Class 10 Maths Chapter 8 Trigonometry Exercise 8.4 Q5.6
NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.4 Q5.7

 

Leave a Comment