logo
Log in
  Get Rs 200 off on Oswal Premium Plan for your board preperatoin! For Class 9th till 12th. Use Coupon Code BOARD200 at checkout.
logo
Log in
Start Free Trial
Trigonometry

Home / Board / ICSE / important Questions / Class 10 / Maths / Trigonometry

Class 10 Maths Chapter 18
Trigonometry
Important Questions

exam preparation with oswal.io
In Class 10 ICSE (Indian Certificate of Secondary Education) mathematics, Chapter 2 may not specifically cover the topic of “Banking” as its primary focus. Instead, the curriculum typically includes topics related to commercial mathematics, which can encompass banking concepts. Commercial mathematics includes areas such as simple interest, compound interest, and profit and loss, which are essential aspects of banking and finance. Here are trigonometric identities class 10 ICSE important questions.

Introduction

In Class 10 ICSE (Indian Certificate of Secondary Education) mathematics, the chapter on “Trigonometry” is a fundamental topic that explores the relationships between angles and sides of right triangles. Trigonometry is a branch of mathematics that has wide-ranging applications, including in navigation, engineering, physics, and more. Here’s an introduction to trigonometry in Class 10 ICSE mathematics: Importance of Trigonometry: Trigonometry is a critical branch of mathematics because it helps us solve real-world problems involving angles and distances. It’s especially valuable in fields that require precise measurements and calculations. Common Trigonometric Formulas: Trigonometric Identities: These include the Pythagorean identities (sin^2θ + cos^2θ = 1) and various angle sum and difference identities. Special Angles: Trigonometry deals with special angles like 30 degrees, 45 degrees, and 60 degrees, which have well-defined trigonometric values.

What is Trigonometry?

Trigonometry is the study of the relationships between the angles and sides of triangles. It primarily focuses on right triangles, which have one angle equal to 90 degrees. Trigonometric functions and ratios, such as sine, cosine, and tangent, are used to establish these relationships. Key Concepts and Objectives:
Trigonometric Ratios: The fundamental trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). They relate the angles of a right triangle to the lengths of its sides.
Right Triangles: Trigonometry primarily deals with right triangles, where one angle is 90 degrees. The side opposite the right angle is the hypotenuse, and the other two sides are the legs.
Sine, Cosine, and Tangent: These trigonometric ratios are defined as follows:
Sine (sin): Opposite side / Hypotenuse
Cosine (cos): Adjacent side / Hypotenuse
Tangent (tan): Opposite side / Adjacent side
trigonometry class 10 icse important questions

Class 10 Trigonometry Important Questions and Answers

Q1. \space \space \frac{cos A}{1-sin A} - tan A =
Options
(a) cos A
(b) sec A
(c) sin A
(d) cosec A

Ans. (b)
Explanation:
\frac{cos A}{1- sin A} - tan A \\ = \frac{cos A(1+sin A)}{1-sin A(1+ sin A)}- tan A \\ =\frac{cos A(1+ sin A)}{(1+sin^2 A)} -tan A \\ = \frac{cos A(1+ sin A)}{cos^2 A} - tan A \\ = \frac{(1+sin A)}{cos A} -tan A \\ = \frac{1}{cos A} + \frac{sin A}{cos A} - tan A

Q2. \frac{cos A}{1-sin A} -tan A=
Options
(a) Cos A
(b) Sec A
(c) Sin A
(d) Cosec A

Ans. (b)
Explanation:
\frac{cos A}{1-sin A} -tan A = \frac{cos A(1+ sin A)}{(1- sin A)(1+ sin A)} - tan A \\ = \frac{cos A(1+sin A)}{1+sin^2 A} - tan A \\ = \frac{cos A(1+ sin A)}{cos ^2 A} - tan A \\ = \frac{1+ sin A}{cos A} - tan A \\ = \frac{1}{cos A} + \frac{sin A}{cos A} - tan A \\ = sec A + tan A - tan A = sec A.

Q3. Prove that :
(i) \sqrt{\frac{1-cos\theta}{1+cos \theta}} = cosec θ - cos θ \\ (ii) \sqrt{\frac{1+cos \theta}{1-cos \theta}} = sec θ - tan θ

Explanation:
(i) L.H.S.
=\sqrt{\frac{1-cos\theta}{1+cos\theta}×\frac{1-cos\theta}{1-cos\theta}} \\ =\sqrt{\frac{(1-cos\theta)^2}{1+cos^2\theta}} \\ =\frac{1-cos\theta}{\sqrt{1-cos^2\theta}} \\ =\frac{1-cos\theta}{\sqrt{sin^2\theta}} \\ =\frac{1-cos \theta}{sin \theta}\\ =\frac{1}{sin \theta}-\frac{cos \theta}{sin \theta} \\ = cosec θ – cot θ \\ \text{= R.H.S. Hence Proved.} \\ \text{(ii)L.H.S.=} \sqrt{\frac{1+sin \theta}{1-sin\theta}×\frac{1+sin \theta}{1+sin\theta}} \\ =\sqrt{\frac{(1+sin\theta)^2}{1-sin^2\theta}} \\ = \frac{1+sin\theta}{cos\theta} = \frac{1}{cos\theta} + \frac{sin\theta}{cos \theta} \\ = sec θ + tan θ = R.H.S. Hence Proved

Q4. Prove that :
sin^4 θ – cos^4 θ = sin^2θ – cos^2θ = 2 sin^2θ – 1 = 1 – 2 cos^2θ.

Explanation:
Consider,
sin^4θ – cos^4θ = (sin^2 θ)^2 – (cos^2 θ)^2 \\ = (sin^2 θ – cos^2θ)(sin^2θ + cos^2θ) [∵ (a – b)(a + b) = a^2– b^2] \\ = (sin^2 θ – cos^2θ) × 1 [∵ sin^2θ+ cos^2θ= 1] \\ = sin^2θ – cos^2θ \\ = sin^2θ – (1 – sin^2θ) [∵cos^2θ = 1 – sin^2θ] \\ = sin^2θ – 1 + sin^2θ \\ = 2 sin^2θ – 1 \\ = 2(1 – cos^2θ) – 1 [∵ sin^2θ =1 – cos^2θ] \\ = 2 – 2 cos^2θ – 1 \\ = 1 – 2 cos^2θ. Hence Proved.

Q5. The angle of elevation of a cloud from a point 200 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud.

Explanation:
Let P be the point of observation and C, the position of cloud. CN perpendicular from C on the surface of the lake and C‘ be the reflection of the cloud in the lake so that

Trigonometry_Q5

CN = NC´ = x (say)
Then, PM = 200 m
∴   AN = MP = 200 m
CA = CN – AN
= (x – 200) m
C´A = NC´ + AN
= (x + 200) m
Let PA = y m
Then, in right angled Δ  PAC,
\frac{CA}{PA} =tan 30 \\ ⟹ \frac{x+200}{y} = \sqrt{3} \\ ⇒x + 200 = \sqrt{3}y \\ ⟹ y = \frac{y+200}{\sqrt{3}} ...(ii) \\ \text{From equations (i) and (ii),}\\ \frac{x+200}{y} = \sqrt{3} (x-200)\\ ⇒   x+200 = 3(x–200)
⇒   x+200 = 3x–600
⇒   2x = 800
⇒   x = 400 m‍
Hence, the height of the cloud = 400 m.

Want to Master this Chapter?
Our Practice Tests, Mind Maps, and Key Questions will help!

Download Mind Map of this chapter

Download Now

Want to Practice Mock Tests of this chapter

Practice Now

Download Important Questions of this chapter

Download Now
Want to Master this Chapter?
Our Practice Tests, Mind Maps, and Key Questions will help!
Download Mind Map of this chapter
Download Now
Want to Practice Mock Tests of this chapter
Practice Now
Download Important Questions of this chapter
Download Now

ICSE Class 10 Maths Chapter wise Important Questions

Chapter No.Chapter Name
Chapter 1Goods and Service Tax (GST)
Chapter 2Banking
Chapter 3Shares and Dividends
Chapter 4Linear inequations
Chapter 5Quadratic Equations in one variable
Chapter 6Ratio and proportion
Chapter 7Factorization
Chapter 8Matrices
Chapter 9Arithmetic Progression
Chapter 10Geometric Progression
Chapter 11Coordinate Geometry
Chapter 12Reflection
Chapter 13Similarity
Chapter 14Loci
Chapter 15Circles
Chapter 16Constructions
Chapter 17Mensuration
Chapter 18Trigonometry
Chapter 19Statistics
Chapter 20Probability

Conclusion

The study of trigonometry in Class 10 ICSE mathematics is essential for understanding the relationships between angles and sides in right triangles. It equips students with tools to solve practical problems and lays the foundation for more advanced mathematics and scientific applications. If you seek additional practice and a deeper comprehension of the topics covered in the chapter, oswal.io offers an extensive array of class 10 Trigonometry important questions and answers to facilitate a more profound understanding of the concepts.

Frequently Asked Questions

Ans: Trigonometry is the study of the relationships between angles and sides in triangles. It’s important because it helps us solve real-world problems involving measurements, distances, and angles.
Ans: The primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).
Ans: The sine (sin) of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Ans: The cosine (cos) of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Ans: The tangent (tan) of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
logo
Instagram Linkedin-in Facebook-f Youtube Twitter
logo
Instagram Linkedin-in Facebook-f Youtube Twitter

CBSE Important Questions Class 10

ICSE Important Questions Class 10

CBSE Important Questions Class 10

ICSE Important Questions Class 10

Contact Us

© Copyright 2025 oswal.io by
Oswal Publishers Simplifying Exams