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Chapters
1: Rational and Irrational Numbers
UNIT-II: COMMERCIAL MATHEMATICS
2: Compound Interest
UNIT-III: ALGEBRA
3: Expansions
4: Factorisation
5: Simultaneous Linear Equations
6: Indices
7: Logarithms
UNIT-IV: GEOMETRY
8: Triangles
9: Inequalities
10: Mid-point Theorem
11: Pythagoras Theorem
12: Rectilinear Figures (Theorems on Parallelograms and Construction of Polygons)
13: Theorems on Area
14: Circles (Chord and Arc Properties)
UNIT-V: STATISTICS
15: Statistics
16: Graphical Representation of Statistical Data
UNIT-VI: MENSURATION
17: Mensuration
18: Surface Area and Volume of Solids
UNIT-VII: TRIGONOMETRY
▶ 19: Trigonometry
20: Simple 2-D Problems in Right Triangle
UNIT-VIII: COORDINATE GEOMETRY
21: Coordinate Geometry
![B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 19 - Trigonometry - Shaalaa.com](/images/mathematics-english-class-9-icse_6:a927b361d63845f4b2afea4ec6bbe35a.jpg "B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 19 - Trigonometry")
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Solutions for Chapter 19: Trigonometry
Below listed, you can find solutions for Chapter 19 of CISCE B Nirmala Shastry for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई.
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 19 Trigonometry EXERCISE 19A [Page 231]
Find sin θ, cos θ and tan (90° - θ).
Find sin(90° - θ), cos θ and tan θ.
If sin θ = `5/13` and AC = 52 cm, find AB, BC and tan θ.
If cos θ = 0.96 and AB = 24 cm, find BC, AC and cot θ.
Find cos α and sin β.
Find sin θ + cos θ, and sec α + tan α in the following figure.
Find sec x + tan x
cosy − sin y
Find tan θ + cot α, sin θ, cos α.
If cos θ = `11/61`, find tan θ.
If sin θ = `5/13`, find sec θ + tan θ.
If sin θ = 0.6, find sec θ + tan θ.
If cos θ = 0.28, find cosec θ - cot θ.
If 12 sin θ = 35 cos θ, find `(sin θ − cos θ)/(sin θ + cos θ)`
12 cos θ - 16 sin θ = 0, find 2 sin θ + cos θ.
If tan θ = `p/q,` show that `(p sin θ – q cos θ)/(p sin θ + q cos θ) = (p^2 − q^2)/(p^2 + q^2)`
If sin A = `3/5 and cos B = 12/13`, evaluate:
sec2A
If sin A = `3/5 and cos B = 12/13`, evaluate:
tan A + tan B
If 5 tan θ = 4, find the value of `(5 sin θ − 3 cos θ)/(5 sin θ + 2 cos θ)`
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 19 Trigonometry EXERCISE 19B [Page 233]
Find the angle θ in the following, if 0° < θ < 90°.
sin θ = cos 75°
Find the angle θ in the following, if 0° < θ < 90°.
cos θ = sin 48°
Find the angle θ in the following, if 0° < θ < 90°.
cos θ = sin θ
Find the angle θ in the following, if 0° < θ < 90°.
cos 2θ = sin θ
Find the angle θ in the following, if 0° < θ < 90°.
tan `θ/2 = cot 2θ`
Find the angle θ in the following, if 0° < θ < 90°.
sin (2θ − 10°) = cos (θ + 40°)
Evaluate without using a trigonometric table:
`(3 sin 23°)/(cos 67°) − (tan 64°)/(cot 26°)`
Evaluate without using a trigonometric table:
`(Cos70°)/(sin20°)` + cos 36° cosec 54°
Evaluate without using a trigonometric table:
`(cot 38°)/(tan 52°) + (sec 25°)/("cosec" 65°) − (3 tan 35°)/(cot 55°)`
Evaluate without using a trigonometric table:
`sin 48° sec 42° + (sec 50°)/ ("cosec" 40°)`
Evaluate without using a trigonometric table:
Cos 20° cosec 70° + `(tan34°)/(cot56°)`
Evaluate without using a trigonometric table:
`(3 sin 32°)/(cos 58°) + (4 tan 46°)/(cot 44°) − (5 sec 62°)/("cosec" 28°)`
Evaluate without using a trigonometric table:
`(2 tan 36°)/(cot 54°) + (3 cot 38°)/(tan 52°) − (2 sec 41°)/("cosec" 49°)`
Evaluate without using a trigonometric table:
`(sin 32° cos 58° + cos 32° sin 58°)/(tan20° tan 70°)`
Evaluate without using a trigonometric table:
cos 44° cosec 46° + tan 30° tan 60° − `sqrt2` cos 45° + tan2 60°
Simplify:
sin θ sin (90° − θ) − cos θ cos (90° − θ)
Simplify:
cot (90° − θ) x `sin (90° − θ)/cos (90° − θ)`
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 19 Trigonometry EXERCISE 19C [Pages 236 - 237]
Find the value of:
(2 cos 0° + sin 45°)(tan 45° − cos 45° + sin 90°)
Find the value of:
`(4 sin 60° + (cos 60°)/(sin 30°)) (4 cos 30° − 2 sin 30°)`
Find the value of:
`4 (sin^2 30° + cos^2 60°) − 3 (cos^2 45° − 1/2 sin^2 90°)`
Find the value of:
1 – 2 cos2 60° + sin 30°
Find the value of:
2 tan2 30° − tan2 45° + tan2 60°
Find the value of:
`(2 cos 30°)/(cos^2 45°) + (tan 60°)/(sin 60° xx tan 30°)`
Find the value of:
`sqrt((1-sin^2 30°)/(1- cos^2 30°))`
Find the value of:
tan2 60° cosec2 45° + sec2 60° sin 30°
Find θ if 0° < θ ≤ 90°.
2 sin2 θ + cos2 45° = tan2 45°
Find θ if 0° < θ ≤ 90°.
sin θ = `(2 tan 30°)/(1 + tan^2 30°)`
Find θ if 0° < θ ≤ 90°.
cos θ = 4 cos3 30° − 3 cos 30°
Find θ if 0° < θ ≤ 90°.
tan θ = sin 30° cos 60° + cos 30° sin 60°
Find θ if 0° < θ ≤ 90°.
sin θ = 3 sin 30° − 4 sin3 30°
Find θ if 0° < θ ≤ 90°.
cos θ = cos 60° cos 30° + sin 60° sin 30°
Find θ if 0° < θ ≤ 90°.
`sin^2 θ + cos^2 30° = 5/4`
Find θ if 0° < θ ≤ 90°.
cos θ = 2 cos2 30° − 1
Find the measure of angle θ in the following when θ is acute.
sin `(θ/3 + 10°) = 1/2`
Find the measure of angle θ in the following when θ is acute.
2 cos2 5θ = 1
Find the measure of angle θ in the following when θ is acute.
tan 3θ − 1 = 0
Find the measure of angle θ in the following when θ is acute.
4 cos2 θ − 3 = 0
show that 4 cos3 θ − 3 cos θ = cos 3θ
Find the measure of angle θ in the following when θ is acute.
3 tan2 θ = 1
show that `(2 tan θ)/(1− tan^2 θ )= tan 2θ`
Find the measure of angle θ in the following when θ is acute.
2 sin θ − 1 = 0
show that sin 3θ = 3 sin θ − 4 sin3 θ
Find the measure of angles A and B in the following, where A and B are acute.
sin (A+ B) = `sqrt3/2 and cos 2A = 1/2`
Find the measure of angles A and B in the following, where A and B are acute.
2 cos 3B = 1 and sin (A + B) = 1
Find the measure of angles A and B in the following, where A and B are acute.
cos `((A + B)/2) = 1/ sqrt2 and 2 sin (A − B) = 1`
Find the measure of angles A and B in the following, where A and B are acute.
2 sin (2A − B) = 1 and tan `((2A + B)/2) = 1/sqrt3`
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 19 Trigonometry MULTIPLE CHOICE QUESTIONS. [Pages 237 - 238]
sin 30° − tan 45° + cos 60° is ______.
0
−1
`sqrt3/2`
2
4 tan 45° – 2 cos 60°
0
4 − `sqrt3`
3
2
cos2 30° + sin2 30°
`sqrt3/2 + 1/4`
`5/4`
1
`(sqrt3 + 1)/2`
tan2 30° − tan2 45° + tan2 60°
`2 1/3`
`8 1/3`
`−3 2/3`
0
sec 60° − sin2 30°
`2/sqrt3 − 1/4`
`1 3/4`
`1 1/2`
`2 1/4`
cos2 45° − sin2 90°
0
`1/2`
`− 1/2`
1
`(sin 60°)/(tan 60°)`
`sqrt3/2`
`1/2`
`1/sqrt3`
`sqrt3`
3 sin2 45° + 2 cos2 60° + cot2 30°
1
2
3
5
cos2 45° + sin2 60° + sin2 30° = ______.
1
`1 1/4`
`1 1/2`
`1 1/3`
cos 0° + sec 60° = ______.
2
3
1
`1 1/2`
sec θ + tan θ = ______.
0
1
2
3
sinθ + cosθ = ______.
1
`1 2/5`
2
3
sin B + tan C = ______.
`1/2`
`17/15`
`4/3`
`3/4`
If 3 sin θ = 4 cos θ, then cot θ = ______.
`3/4`
`4/3`
`1/5`
`7/5`
sin 43° = cos θ, ∴ θ = ______.
43°
47°
57°
133°
5 tan θ = 4, ∴ sin θ = ______.
4
`4/3`
`4/sqrt41`
`3/4`
cos 2θ = sin θ, ∴ θ = ______.
0°
90°
60°
30°
tan 3θ = 1, ∴ θ = ______.
45°
15°
20°
10°
cos2 θ = `3/4` ∴ θ = ______.
60°
45°
30°
90°
If θ = 30° then 3 sin θ − 4 sin3 θ = ______.
0
−1
1
`−1/2`
Direction for Questions 21 to 27: In each of the following questions, a statement of assertion (A) is given and a statement of Reason (R) given below it choose the correct option for each question.
Assertion (A): In ΔABC, ∠B = 90°, sin C = 0.6, then cos A = 0.8.
Reason (R): sin C = cos (90 − C) = cos A.
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A
A is true but R is false.
A is false but R is true.
Assertion (A): tan 23° tan 45° tan 67° = 1.
Reason (R): tan 23° tan 67° = tan 23° cot(90° − 67°) = tan 23° cot 23° = 1 and tan 45° = 1.
Both A and R are true and R is the correct reason for A.
Both A and Rare true but R is the incorrect reason for A
A is true but R is false.
A is false but R is true.
Assertion (A): If 2 sin2 θ = 1 then θ = 30°.
Reason (R): sin 30° = `1/2`.
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion (A): tan2 60° × sec2 45° = 6.
Reason (R): tan 60° = `sqrt3, cos 45° = 1/sqrt2`
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion (A): sin2 42° + sin2 48° = 1
Reason (R): sin2 42° + sin2 48° = sin2 (42° + 48°) = sin2 90° = 1
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion (A): 5 tan θ = 4 then sin θ = 4, cos θ = 5
Reason (R): tan θ = `sin θ/cos θ`
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion (A): If tan A = 1, then 2 sin A cos A= 1
Reason (R): tan 45° = 1
Both A and R are true and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 19 Trigonometry MISCELLANEOUS EXERCISE [Page 239]
Find the value of the following without using a table:
tan 30° × tan 60° + cos 0° + sec 60°
Find the value of the following without using a table:
sin2 30° + cos2 60° + cosec 30°
Do as directed:
2 cos2 θ − 1 = 0, find θ, tan θ, sin 2θ and sin2 θ.
Do as directed:
sin θ = 0.96, find the value of cot θ + cosec θ.
Find the angle θ, when 0° < θ < 90°.
3 tan2 (θ + 10°) = 1, 0° < θ < 90°
Find the angle θ when 0° < θ < 90°.
(tan2 θ − 3)(2 sin 3θ − 1) = 0
Find the angle θ, when 0° < θ < 90°.
cos θ = cos2 30° − sin2 30°
Find the angle θ when 0° < θ < 90°.
sin 8 = 2 sin 30° cos 30°
Evaluate the following without using a table:
`2 (tan 32°)/(cot 58°) + (sec 46°)/("cosec" 44°)`
Evaluate the following without using a table:
3 tan 28° tan 62° − `(sec 36°)/("cosec" 54°) + (sin 28°)/(cos 62°)`
Evaluate the following without using a table:
sin 34° sec 56° + 4 cos 43° cosec 47°
Evaluate the following without using a table:
`(sin 42°)/(sec 48°) + (cos 42°)/("cosec" 48°)`
Evaluate the following without using a table:
`(sec 17°)/("cosec" 73°) + (tan 68°)/(cot 22°)` + cos 44° cosec 46°
Evaluate the following without using a table:
`(sin 35° cos 55° + cos 35° sin 55°)/("cosec" 10° cos 80°)`
Evaluate the following without using a table:
`(tan 36°)/(cot 54°)` + sin 26° sec 64°
Without using tables, evaluate the following: 4(sin430° + cos460°) - 3(cos245° - sin290°).
Evaluate the following without using a table:
2 tan 18° tan 72° − cot2 30° + cos 34° cosec 56°
Evaluate tan 35° tan 40° tan 45° tan 50° tan 55°
In the figure given alongside, AB = 6 cm, AC = 10 cm, ∠B = 90° and EC = 21 cm.
Find:
- AD and AE
- cos θ + sin θ
- cot α + cosec α.
In the given figure, find the value of
- sin α + cos α
- tan β − cosec β
Solutions for 19: Trigonometry
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 19 - Trigonometry
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Concepts covered in मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 19 Trigonometry are Concept of Perpendicular, Base, and Hypotenuse in a Right Triangle, Notation of Angles, Trigonometric Ratios, Relation Among Trigonometric Ratios, Trigonometric Equation Problem and Solution, Trigonometric Ratios of Specific Angles.
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