Trigonometry

Important Questions

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.

Table of Contents

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.

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

Sine (sin): Opposite side / Hypotenuse

Cosine (cos): Adjacent side / Hypotenuse

Tangent (tan): Opposite side / Adjacent side

(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

(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.

**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

**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.

**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

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.

Chapter No. | Chapter Name |
---|---|

Chapter 1 | Goods and Service Tax (GST) |

Chapter 2 | Banking |

Chapter 3 | Shares and Dividends |

Chapter 4 | Linear inequations |

Chapter 5 | Quadratic Equations in one variable |

Chapter 6 | Ratio and proportion |

Chapter 7 | Factorization |

Chapter 8 | Matrices |

Chapter 9 | Arithmetic Progression |

Chapter 10 | Geometric Progression |

Chapter 11 | Coordinate Geometry |

Chapter 12 | Reflection |

Chapter 13 | Similarity |

Chapter 14 | Loci |

Chapter 15 | Circles |

Chapter 16 | Constructions |

Chapter 17 | Mensuration |

Chapter 18 | Trigonometry |

Chapter 19 | Statistics |

Chapter 20 | Probability |

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.

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.

Chapter Wise Important Questions for ICSE Board Class 10 Mathematics |
---|

Goods and Service Tax (GST) |

Banking |

Shares and Dividends |

Linear inequations |

Quadratic Equations in one variable |

Ratio and proportion |

Factorization |

Matrices |

Arithmetic Progression |

Geometric Progression |

Coordinate Geometry |

Reflection |

Similarity |

Loci |

Circles |

Constructions |

Mensuration |

Trigonometry |

Statistics |

Probability |

CBSE Important Questions Class 9

CBSE Important Questions Class 10

CBSE Important Questions Class 12

- CBSE Class 12 English
- CBSE Class 12 Maths
- CBSE Class 12 Physics
- CBSE Class 12 Biology
- CBSE Class 12 Chemistry
- CBSE Class 12 Computer Science
- CBSE Class 12 Business Study
- CBSE Class 12 Economics
- CBSE Class 12 Physical Education

CBSE Practice Papers

CBSE Practice Papers

ICSE Important Questions Class 9

- ICSE Class 9 Maths
- ICSE Class 9 Physics
- ICSE Class 9 Chemistry
- ICSE Class 9 Biolog1y
- ICSE Class 9 History & Civics
- ICSE Class 9 Geography
- ICSE Class 9 Computer Applications

ICSE Important Questions Class 10

ICSE Practice Papers

- ICSE Class 10 Physics
- ICSE Class 10 Chemistry
- ICSE Class 10 Biology
- ICSE Class 10 Maths

ISC Important Questions Class 12

- ISC Class 12 Physics
- ISC Class 12 Chemistry
- ISC Class 12 Biology
- ISC Class 12 Maths
- ISC Class 12 Economics
- ISC Class 12 Physical Education
- ISC Class 12 Computer Science

ISC Practice Papers

- ISC Class 12 Physics
- ISC Class 12 Chemistry
- ISC Class 12 Biology
- ISC Class 12 Maths

Contact Us

Noida - 201309, Uttar Pradesh

© Copyright 2024 **oswal.io** by **OSWAL PUBLISHERS** Simplifying Exams