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Inverse Trigonometric Functions

Madhya Pradesh Board · Class 12 · Mathematics

Complete topic list for Inverse Trigonometric Functions in Madhya Pradesh Board Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

105 questions44 flashcards5 concepts

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A flowchart illustrating the conditions (one-one and onto) required for a function to have an inverse, and what happens if these conditions are not met.
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4 Topics · Madhya Pradesh Board Class 12 Mathematics

Topics in Inverse Trigonometric Functions

1

1. Basic ideas and principal value branches

  • A function has an inverse only when it is one-one and onto.
  • Sine, cosine, secant, cosecant, tangent, and cotangent are not one-one over their natural domains.
  • By restricting the domain, inverse trigonometric functions are defined.
2

2. Domains and principal value ranges

  • sin is one-one on [-π/2, π/2] and has range [-1, 1].
  • cos is one-one on [0, π] and has range [-1, 1].
  • cosec is one-one on [-π/2, π/2] - {0} and has range R - (-1, 1).
3

3. Standard principal values and worked examples

  • The principal value of sin⁻¹(1/√2) is π/4.
  • The principal value of cot⁻¹(-1/√3) is 2π/3.
  • For sin⁻¹(sin x), the answer must be reduced to the principal branch if needed.
4

4. Important identities and simplification patterns

  • Inverse trigonometric expressions are often simplified by substitution.
  • Trigonometric double-angle and triple-angle ideas are useful in inverse problems.
  • Some expressions become simple after using half-angle identities.

Key Concepts

Central concept: Inverse trigonometric functions are defined by restricting trigonometric functions to principal value branches so that the functions become one-one and onto, allowing inverse functions to exist and be used correctly within their domains.

Inverse function ideaPrincipal value branchsin inversecos inversecosec inversesec inversetan inversecot inverse

Frequently Asked Questions

What are the important topics in Inverse Trigonometric Functions for Madhya Pradesh Board Class 12 Mathematics?
Inverse Trigonometric Functions covers several key topics that are frequently asked in Madhya Pradesh Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Inverse Trigonometric Functions — Madhya Pradesh Board Class 12 Mathematics?
Understand the core concepts first, then work through the 105 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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