Q583: Domain of $f(x)=\cos^{-1}x+\sin x$ is :...

Class CBSE Class 12 Mathematics Inverse Trigonometric Functions Q #583

KNOWLEDGE BASED

APPLY

1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE

Domain of $f(x)=\cos^{-1}x+\sin x$ is :

(A) R

(B) $(-1, 1)$

(D) $[-\pi/2, \pi/2]$

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AI Tutor Explanation

Detailed Solution

Step 1: Identify the domain of cos^-1x

The domain of the inverse cosine function, $\cos^{-1}x$, is the set of all real numbers $x$ such that $-1 \le x \le 1$. This can be written as $x \in [-1, 1]$.

Step 2: Identify the domain of sin x

The domain of the sine function, $\sin x$, is the set of all real numbers. This can be written as $x \in \mathbb{R}$.

Step 3: Find the domain of f(x)

The domain of the function $f(x) = \cos^{-1}x + \sin x$ is the intersection of the domains of $\cos^{-1}x$ and $\sin x$. Since the domain of $\cos^{-1}x$ is $[-1, 1]$ and the domain of $\sin x$ is $\mathbb{R}$, the intersection is $[-1, 1]$.

Final Answer: [-1, 1]

AI Suggestion: Option C

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Pedagogical Audit

Bloom's Analysis: This is an APPLY question because the student needs to apply their knowledge of the domains of inverse trigonometric functions and trigonometric functions to find the domain of the given function.

Knowledge Dimension: CONCEPTUAL

Justification: The question requires understanding the concept of the domain of trigonometric and inverse trigonometric functions and how to find the domain of a function that is a combination of these functions.

Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of the domains of trigonometric and inverse trigonometric functions, which is a standard topic in the syllabus.