NCERT Solutions Class 10 Mathematics Chapter 8 Introduction To Trigonometry Download In Pdf

Chapter 8 Introduction To Trigonometry Download in pdf

EXERCISE 8.1

**Question 1.** In Î” ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine :

(i) sin A, cos A

(ii) sin C, cos C

**Question 2.** In Fig. 8.13, find tan P â€“ cot R.

**Question 3.** If sin A =
3 ,
4
calculate cos A and tan A.

**Question 4. **Given 15 cot A = 8, find sin A and sec A.

**Question 5.** Given sec Î¸ =
13 ,
12
calculate all other trigonometric ratios.

**Question 6.** If âˆ A and âˆ B are acute angles such that cos A = cos B, then show that âˆ A = âˆ B.

**Question 7.** If cot Î¸ =
7 ,
8
evaluate :

(i)
(1 sin ) (1 sin ) ,
(1 cos ) (1 cos )
+ Î¸ âˆ’ Î¸
+ Î¸ âˆ’ Î¸

(ii) cot2 Î¸

**Question 8.** If 3 cot A = 4, check whether
2
2
1 tan A
1 + tan A
âˆ’
= cos2 A â€“ sin2A or not.

**Question 9.** In triangle ABC, right-angled at B, if tan A =
1 ,
3
find the value of:
(i) sin A cos C + cos A sin C
(ii) cos A cos C â€“ sin A sin C

**Question 10.** In Î” PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of
sin P, cos P and tan P.

**Question 11.** State whether the following are true or false. Justify your answer.

(i) The value of tan A is always less than 1.

(ii) sec A =
12
5 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 Î¸ =
4
3 for some angle Î¸.

EXERCISE 8.2

**Question 1. **Evaluate the following :

(i) sin 60Â° cos 30Â° + sin 30Â° cos 60Â°

(ii) 2 tan2 45Â° + cos2 30Â° â€“ sin2 60Â°

**Question 3.** If tan (A + B) = 3 and tan (A â€“ B) =
1
3 ; 0Â° < A + B â‰¤ 90Â°; A > B, find A and B.

**Question 4.** State whether the following are true or false. Justify your answer.

(i) sin (A + B) = sin A + sin B.

(ii) The value of sin Î¸ increases as Î¸ increases.

(iii) The value of cos Î¸ increases as Î¸ increases.

(iv) sin Î¸ = cos Î¸ for all values of Î¸.

(v) cot A is not defined for A = 0Â°.

EXERCISE 8.3

**Question 1.** Evaluate :

(i)
sin 18
cos 72
Â°
Â°

(ii)
tan 26
cot 64
Â°
Â°

(iii) cos 48Â° â€“ sin 42Â°

(iv) cosec 31Â° â€“ sec 59Â°

**Question 2.** Show that :

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

(ii) cos 38Â° cos 52Â° â€“ sin 38Â° sin 52Â° = 0

**Question 3.** If tan 2A = cot (A â€“ 18Â°), where 2A is an acute angle, find the value of A.

**Question 4.** If tan A = cot B, prove that A + B = 90Â°.
5. If sec 4A = cosec (A â€“ 20Â°), where 4A is an acute angle, find the value of A.

EXERCISE 8.4

**Question 1.** Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

**Question 2. **Write all the other trigonometric ratios of âˆ A in terms of sec A.

**Question 3.** Evaluate :

(i)
2 2
2 2
sin 63 sin 27
cos 17 cos 73
Â° + Â°
Â° + Â°

(ii) sin 25Â° cos 65Â° + cos 25Â° sin 65Â°

**Question 4.** Choose the correct option. Justify your choice.

(i) 9 sec2 A â€“ 9 tan2 A =

(A) 1

(B) 9

(C) 8

(D) 0

(ii) (1 + tan Î¸ + sec Î¸) (1 + cot Î¸ â€“ cosec Î¸) =

(A) 0

(B) 1

(C) 2

(D) â€“1

(iii) (sec A + tan A) (1 â€“ sin A) =

(A) sec A

(B) sin A

(C) cosec A

(D) cos A

(iv)
2
2
1 tan A
1 + cot A
+
=

(A) sec2 A

(B) â€“1

(C) cot2 A

(D) tan2 A

**Question 5.** Prove the following identities, where the angles involved are acute angles for which the
expressions are defined.

(i) (cosec Î¸ â€“ cot Î¸)2 =
1 cos
1 cos
âˆ’ Î¸
+ Î¸

(ii) cos A 1 sin A 2 sec A

(iii)
tan cot 1 sec cosec
1 cot 1 tan
Î¸ Î¸
+ = + Î¸ Î¸
âˆ’ Î¸ âˆ’ Î¸
[Hint : Write the expression in terms of sin Î¸ and cos Î¸]

(iv)
1 sec A sin2 A
sec A 1 â€“ cos A
+
= [Hint : Simplify LHS and RHS separately]

(v) cos A â€“ sin A + 1 cosec A + cot A,
cos A + sin A â€“ 1
= using the identity cosec2 A = 1 + cot2 A.

(vi)
1 sinA sec A + tan A
1 â€“ sin A
+
=

(vii)
3
3
sin 2 sin tan
2 cos cos
Î¸ âˆ’ Î¸
= Î¸
Î¸ âˆ’ Î¸

(viii) (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A

(ix)
(cosec A â€“ sin A)(sec A â€“ cos A) 1
tanA + cot A
=
[Hint : Simplify LHS and RHS separately]

(x)
2 2
2
1 tan A 1 tanA
1 + cot A 1 â€“ cot A
= tan2 A

Please send your queries to ncerthelp@gmail.com you can aslo visit our facebook page to get quick help. Link of our facebook page is given in sidebar

- Chapter 3 Pair of Linear Equations In Two Variables
- Chapter 4 Quadratic Equations
- Chapter 7 Coordinate Geometry
- Chapter 8 Introduction To Trigonometry
- Chapter 11 Constructions
- Chapter 9 Some Applications of Trigonometry
- chapter 10 Circles
- Chapter 12 Areas Related To Circles
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability
- Chapter 5 Arithmetic Progressions

- NCERT Solutions for Class 9 Science Maths Hindi English Math
- NCERT Solutions for Class 10 Maths Science English Hindi SST
- Class 11 Maths Ncert Solutions Biology Chemistry English Physics
- Class 12 Maths Ncert Solutions Chemistry Biology Physics pdf

- Class 1 Model Test Papers Download in pdf
- Class 5 Model Test Papers Download in pdf
- Class 6 Model Test Papers Download in pdf
- Class 7 Model Test Papers Download in pdf
- Class 8 Model Test Papers Download in pdf
- Class 9 Model Test Papers Download in pdf
- Class 10 Model Test Papers Download in pdf
- Class 11 Model Test Papers Download in pdf
- Class 12 Model Test Papers Download in pdf

Copyright @ ncerthelp.com A free educational website for CBSE, ICSE and UP board.