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Assertion & Reason (A&R) questions consist of two statements: the Assertion (A) and the Reason (R). Students must analyze:
Whether the Assertion is true or false
Whether the Reason is true or false
If the Reason correctly explains the Assertion
These questions test both theoretical understanding and logical reasoning in mathematics, particularly in the topic of inverse trigonometric functions.
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♦ Mathematics :
♦ Relations and Functions ⇒ Download Here
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♦ Determinants ⇒ Download Here
♦ Continuty and Differentiablity ⇒ Download Here
♦ Application of Derivatives ⇒ Download Here
♦ Integrals ⇒ Download Here
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♦ Differential Equations ⇒ Download Here
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CBSE includes Assertion & Reason questions to:
Evaluate conceptual understanding rather than rote memorization
Test analytical thinking and reasoning abilities
Identify misconceptions in inverse trigonometric concepts
Prepare students for competitive exams that emphasize logical reasoning
Topics like principal values, properties, and compositions of inverse trigonometric functions are frequently covered.
There are four main types of Assertion & Reason questions:
Both Assertion and Reason are true, and Reason correctly explains Assertion
Both Assertion and Reason are true, but Reason does not explain Assertion
Assertion is true, Reason is false
Both Assertion and Reason are false
Recognizing the type of question helps students approach them with confidence and accuracy.
Carefully read the Assertion and Reason
Determine the truth value of each independently
Verify if the Reason logically explains the Assertion
Apply formulas, identities, and properties of inverse trigonometric functions
Practice regularly to improve speed and accuracy
Key areas include:
Principal Values: Domain and range of inverse trigonometric functions
Properties: Addition and subtraction formulas, function identities
Compositions: Expressions like sin⁻¹(sin x), tan⁻¹(tan x), etc.
Equations: Solving inverse trigonometric equations
Strengthens understanding of inverse trigonometric concepts
Develops logical reasoning and analytical skills
Improves problem-solving ability
Builds confidence for board exams and competitive exams
Example:
Assertion: sin⁻¹(sin 150°) = 30°
Reason: The principal value of sin⁻¹(x) lies in [-90°, 90°].
Solution:
Assertion is true
Reason is true
Reason correctly explains the Assertion
Memorize principal values and properties of all inverse trigonometric functions
Understand composition rules and restrictions
Read both statements carefully before answering
Solve previous years’ CBSE papers and sample questions
Revise formulas and identities frequently
Confusing the value of the inverse function outside its principal range
Ignoring key terms like "always" or "never"
Relying only on memorization without understanding restrictions
Misinterpreting compositions of functions like sin⁻¹(sin x)
NCERT Class 12 Mathematics textbooks
CBSE sample papers and previous year question papers
Online mock tests and quizzes
Revision notes and solved exercises
Assertion & Reason questions on Inverse Trigonometric Functions are an important part of CBSE Class 12 Mathematics exams. They test both conceptual knowledge and logical reasoning. With consistent practice, understanding of principal values, and mastery of function properties, students can confidently solve these questions and improve their exam performance.
