#### Chapters

Chapter 2: Polynomials

Chapter 3: Pair of Linear Equations in Two Variables

Chapter 4: Quadratic Equations

Chapter 5: Arithmetic Progressions

Chapter 6: Triangles

Chapter 7: Coordinate Geometry

Chapter 8: Introduction to Trigonometry

Chapter 9: Some Applications of Trigonometry

Chapter 10: Circles

Chapter 11: Constructions

Chapter 12: Areas Related to Circles

Chapter 13: Surface Areas and Volumes

Chapter 14: Statistics

Chapter 15: Probability

#### NCERT Mathematics Class 10

## Chapter 8: Introduction to Trigonometry

#### Chapter 8: Introduction to Trigonometry Exercise 8.10 solutions [Page 181]

In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine

sin A, cos A

In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine sin C, cos C

In Given Figure, find tan P – cot R.

If `sin A =3/4` , calculate cos A and tan A.

Given 15 cot A = 8. Find sin A and sec A

Given sec θ = `13/12` , calculate all other trigonometric ratios.

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

If cot θ = 7/8 evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`

If cot θ = 7/8, evaluate cot^{2} θ

If 3 cot A = 4, Check whether `((1-tan^2 A)/(1+tan^2 A)) = cos^2 A - sin^2 A` or not

In ΔABC, right angled at B. If tan A = `1/sqrt3` , find the value of

(i) sin A cos C + cos A sin C

(ii) cos A cos C − sin A sin C

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.

State whether the following are true or false. Justify your answer.

The value of tan A is always less than 1.

State whether the following are true or false. Justify your answer.

sec A = 12/5 for some value of angle A.

State whether the following are true or false. Justify your answer.

cos A is the abbreviation used for the cosecant of angle A.

State whether the following are true or false. Justify your answer. cot A is the product of cot and A

State whether the following are true or false. Justify your answer.

sin θ =4/3, for some angle θ

#### Chapter 8: Introduction to Trigonometry Exercise 8.20 solutions [Page 187]

Evaluate the following in the simplest form: sin 60º cos 30º + cos 60º sin 30º

Evaluate the following : 2tan^{2}45° + cos^{2}30° − sin^{2}60°

Evaluate the following : `(cos 45°)/(sec 30° + cosec 30°)`

Evaluate the following

`(sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°)`

Evaluate the following

`(5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30°+cos^2 30°)`

Choose the correct option and justify your choice

`(2 tan 30°)/(1+tan^2 30°)`

sin 60°

cos 60°

tan 60°

sin 30°

Choose the correct option and justify your choice.

`(1- tan^2 45°)/(1+tan^2 45°) `

tan 90°

1

sin 45°

0

Choose the correct option and justify your choice :

sin 2A = 2 sin A is true when A =

0°

30°

45°

60°

Choose the correct option and justify your choice :

`(2 tan 30°)/(1-tan^2 30°)`

cos 60°

sin 60°

tan 60°

sin 30°

If tan (A + B) = `sqrt3` and tan (A – B) = `1/sqrt3` ; 0° < A + B ≤ 90° ; A > B, find A and B.

State whether the following is true or false. Justify your answer.

sin (A + B) = sin A + sin B

True

False

State whether the following is true or false. Justify your answer.

The value of sinθ increases as θ increases

True

False

State whether the following is true or false. Justify your answer.

The value of cos θ increases as θ increases

True

False

State whether the following is true or false. Justify your answer

sinθ = cos θ for all values of θ

True

False

State whether the following are true or false. Justify your answer.

cot A is not defined for A = 0°

True

False

#### Chapter 8: Introduction to Trigonometry Exercise 8.30 solutions [Pages 189 - 190]

Evaluate `(sin 18^@)/(cos 72^@)`

Evaluate `(tan 26^@)/(cot 64^@)`

Evaluate cos 48° − sin 42°

Evaluate cosec 31° − sec 59°

Show that tan 48° tan 23° tan 42° tan 67° = 1

Show that cos 38° cos 52° − sin 38° sin 52° = 0

If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A

If tan A = cot B, prove that A + B = 90

If sec 4A = cosec (A− 20°), where 4A is an acute angle, find the value of A.

If A, B and C are interior angles of a triangle ABC, then show that `\sin( \frac{B+C}{2} )=\cos \frac{A}{2}`

Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°

#### Chapter 8: Introduction to Trigonometry Exercise 8.40 solutions [Pages 193 - 194]

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

Write all the other trigonometric ratios of ∠A in terms of sec A.

Evaluate

`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`

Evaluate sin25° cos65° + cos25° sin65°

Choose the correct option. Justify your choice.

9 sec^{2} A − 9 tan^{2} A =

1

9

8

0

Choose the correct option. Justify your choice.

(1 + tan θ + sec θ) (1 + cot θ − cosec θ)

0

1

2

-1

Choose the correct option. Justify your choice.

(secA + tanA) (1 − sinA) =

secA

sinA

cosecA

cosA

Choose the correct option. Justify your choice.

`(1+tan^2A)/(1+cot^2A)`

sec

^{2 }A−1

cot

^{2 }Atan

^{2 }A

Prove the following identities, where the angles involved are acute angles for which the expressions are defined

`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined

`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined

`(tantheta)/(1-cottheta) + (cottheta)/(1-tantheta) = 1+secthetacosectheta`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

`(1+ secA)/sec A = (sin^2A)/(1-cosA)`

[Hint : Simplify LHS and RHS separately]

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

`sqrt((1+sinA)/(1-sinA)) = secA + tanA`

`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

(sin A + cosec A)^{2} + (cos A + sec A)^{2} = 7 + tan^{2} A + cot^{2} A

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

(cosec A – sin A) (sec A – cos A)`=1/(tanA+cotA)`

[Hint : Simplify LHS and RHS separately]

`((1+tan^2A)/(1+cot^2A))=((1-tanA)/(1-cotA))^2=tan^2A`

## Chapter 8: Introduction to Trigonometry

#### NCERT Mathematics Class 10

#### Textbook solutions for Class 10

## NCERT solutions for Class 10 Mathematics chapter 8 - Introduction to Trigonometry

NCERT solutions for Class 10 Maths chapter 8 (Introduction to Trigonometry) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Textbook for Class 10 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10 Mathematics chapter 8 Introduction to Trigonometry are Trigonometric Identities, Trigonometric Ratios of Complementary Angles, Trigonometric Ratios, Relationships Between the Ratios, Trigonometric Ratios of Some Specific Angles, Proof of Existence, Trigonometric Ratios of an Acute Angle of a Right-angled Triangle, Introduction to Trigonometry, Introduction to Trigonometry Examples and Solutions.

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