CBSE Ch 2 Important Questions Class 12 Maths 2025 PDF

The reason why the inverse trigonometric functions have a lot of importance is because this is an essential topic of Class 12 Mathematics and can be taken as a base for understanding the application of trigonometry. Inverse trigonometric functions reverse the operations of trigonometry. It also helps greatly to solve most of the problems associated with calculus application, geometry, and many areas of mathematics. Once a student understands the major concepts, properties, and ways of solving for inverse trigonometric functions, it allows the student to get better scores in exams.

Many important questions are framed in board examinations from Mathematics. In Inverse Trigonometry Class 12 Important Questions, you will study the inverse trigonometric functions like sin ^-1, and cos^-1 and various formulas attached to them. 

‍

PREMIUM EDUCART QUESTIONS

<cta2> Download <cta2>

(Most Important Questions of this Chapter from our 📕)

‍

In the table below, we have provided the links to Inverse Trigonometric Functions Class 12 Maths Most Important Questions PDFs for Chapter 2. You can download them without having to share any login info.

Introduction to Inverse Trigonometric Functions

The term arc functions is commonly used for the class of inverse trigonometric functions since these are the quantities that obtain inverses of the following six fundamental trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. They tell what angle, in terms of measurements in angles, has a certain value of the ratio between two known quantities. Some examples are:

• sin⁻¹ x or arcsin(x) for sine,
• cos⁻¹x or arccos(x) for cosine,
• tan⁻¹x or arctan(x) for tangent,
• cot⁻¹x for cotangent,
• sec-1x for secant,
• cosec-1x for cosecant.

Inverse trigonometric functions are great tools for solving angle-measuring applications and working with trigonometric equations. To ensure they are well defined, their domain and range are bounded because the original trigonometric functions are periodic and many-to-one.

Basic Properties of Inverse Trigonometric Functions

Let's understand the key properties and equations used in inverse trigonometric functions before delving into the important questions, as these will serve as a basis for solving more challenging problems.

Domain and Range:

The domain and range for every inverse trigonometric function are defined, so the function is one-to-one and hence invertible.

• sin⁻¹ x: Domain [-1, 1], Range [-π/2, π/2]
• cos⁻¹x: Domain [-1, 1], Range [0, π]
• tan⁻¹x: Domain [-∞, ∞], Range [-π/2, π/2]
• cot⁻¹x: Domain [-∞, ∞], Range [0, π]
• sec-1x: Domain [-∞, -1] U [1, ∞), Range [0, π] \ (π/2)
• cosec⁻¹x: Domain (-∞, -1] U [1, ∞), Range [-π/2, π/2] \ {0}

Key Identities:

• sin⁻¹x + cos⁻¹x = π/2
• tan⁻¹x + cot⁻¹x = π/2
• sec⁻¹x + cosec⁻¹x = π/2

Important Questions

The important questions on the Class 12 inverse trigonometry functions test how well students understand and apply the principles of inverse trigonometric functions.

• Evaluate sin⁻¹ (1/2)
• Find Tan⁻¹ (1)
• Solve the equation sin⁻¹x + cos⁻¹x = π/2.
• Solve for x: tan⁻¹ (2x) = π/4
• Simplify sin⁻¹ (½) + cos⁻¹ (½)
• Simplify sin⁻¹(x) + tan⁻¹(1/x)
• Sketch the graph of y = sin⁻¹x and explain its key features.
• Find the angle θ if sin θ = ⅗ using inverse trigonometric functions.
• Simplify the expression: sin⁻¹(sin x) where -π/2 ≤ x ≤ π/2.
• A ladder is leaning against a wall, forming an angle of 30° with the ground. What is the angle the ladder makes with the wall?
• The angle of elevation of a building from a point is 45 degrees. If the distance from the point to the building is known, use inverse trigonometric functions to determine the height of the building.
• If sin⁻¹(x) = 5π/6, find the value of x.

Significance of Solving Inverse Trigonometric Functions Important Questions

Inverse trigonometric functions hold a very significant place in Class 12 Mathematics. Theoretical and practical applications of these functions are immense. Whether you're preparing for your board exams or want to master mathematics, you must practice all the key questions on inverse trigonometric functions. Let's see why these questions are so important for every student.

Foundation for Advanced Concepts in Mathematics

Inverse trigonometric functions are a crucial part of advanced mathematical topics such as calculus and geometry. Their solutions will reinforce your understanding of concepts such as:

• Derivatives and Integrals
• Applications in Physics and Engineering

Crucial for Solving Trigonometric Equations

Inverse trigonometric functions are the basic tools used in the solution of trigonometric equations, which form a regular part of Class 12 Mathematics. The trigonometric equations frequently demand finding an angle associated with a given trigonometric ratio. Solving problems involving inverse trigonometric functions helps develop many skills, including:

• Identifying and Solving Trigonometric Equations
• Applying Key Identities

Develops Analytical and Problem-Solving Skills

Some questions may require a complicated trigonometric expression to be analysed and transformed into a simpler expression using inverse trigonometric identities. It promotes critical thinking since the students learn how to look at problems from various angles.

Helps in Grasping Graphical Representations

Graphs of inverse trigonometric functions are important to solve any kind of exam question. Solving exercises involving these functions will help the students to have a better sense of their graphical behaviour, which is crucial for:

• Understanding Behaviour and Range
• Interpreting Graphs

Improves Accuracy in Calculations

Many problems with inverse trigonometric functions require precise computations, especially when angles are in radians. Often solving these problems helps students develop their computational skills, especially when:

• Dealing with Values of Special Angles
• Dealing with Exact and Approximate Values

Enhances Conceptual Understanding

Working through significant problems on inverse trigonometric functions helps to fix the basic concepts associated with it. Instead of memorising some formulas, students get a greater insight into:

• The Relationship Between Functions
• Concept of Principal Values
• Understanding Limitations 

Boosts Confidence and Reduces Exam Stress

Confidence is a key determinant of success in exams. Whenever students work on important questions regarding inverse trigonometric functions frequently, they develop an idea of the types of problems they will face during their exams. It reduces their anxiety and boosts their confidence, and hence they feel capable of answering even the most challenging questions on the day of the exam.

With frequent practice, students absorb the content as well as improve their time management skills, thus finishing off the exams efficiently and accurately.

A large portion of the Class 12 Mathematics curriculum revolves around inverse trigonometric functions, which students can't grasp without fully knowing their properties, identities, and ways to solve related problems. The exercise will equip the student for both examination and other learning in mathematics concerning calculating inverses, solving equations, simplification, and graphing. In addition, it is also necessary to remember the basic identities, the domain and range of each function, and the ways to solve equations that contain inverse trigonometric functions.