Are these practice questions for Inverse Trigonometric Functions based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 12 - Science Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Inverse Trigonometric Functions free?

Yes. Every chapter includes free practice questions for Class 12 - Science students to get you started.

What types of questions are included?

The practice set for Inverse Trigonometric Functions mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Inverse Trigonometric Functions for full coverage.

How many practice questions are there for Inverse Trigonometric Functions?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Inverse Trigonometric Functions Class 12 Mathematics Practice Questions with Answers

easy

Determine the domain of the function

f(x) = \sin^{-1}(3x-1)

.

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easy

Justify whether the identity $\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$ holds for $x=1.5$ .

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easy

Calculate the principal value of

\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)

.

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easy

Formulate an expression for $\csc^{-1}(x)$ in terms of $\sin^{-1}$ for $|x| \ge 1$ .

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medium

Analyze and simplify

\tan^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)

for

|x|<a

.

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medium

Calculate the value of

\cos^{-1}\left(\cos\left(\frac{7\pi}{6}\right)\right)

.

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medium

Prove that

$\tan^{-1}\left(\frac{1}{5}\right) + \tan^{-1}\left(\frac{1}{7}\right) + \tan^{-1}\left(\frac{1}{3}\right) + \tan^{-1}\left(\frac{1}{8}\right) = \frac{\pi}{4}$

.

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medium

Critique the following step in a calculation: $\sin^{-1}(\sin(2\pi/3)) = 2\pi/3$ .

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medium

Find the value of the expression

\sin\left(\frac{\pi}{2} - \sin^{-1}\left(-\frac{1}{2}\right)\right)

.

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medium

Calculate the value of

\tan^{-1}(\tan \frac{7\pi}{6})

.

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medium

Simplify the expression

\tan^{-1}\left(\sqrt{\frac{1-\cos x}{1+\cos x}}\right)

for

0 < x < \pi

.

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medium

Solve the equation

\sin^{-1}\frac{5}{x} + \sin^{-1}\frac{12}{x} = \frac{\pi}{2}

.

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medium

Solve for

x

:

\cos(\tan^{-1} x) = \sin(\cot^{-1}\frac{3}{4})

.

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medium

Demonstrate that

\cos^{-1}\frac{4}{5} + \tan^{-1}\frac{3}{5} = \tan^{-1}\frac{27}{11}

.

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medium

Solve the equation:

\tan^{-1}(2x) + \tan^{-1}(3x) = \frac{\pi}{4}

.

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medium

Propose a trigonometric substitution for x to simplify the expression $\tan^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)$ .

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hard

Analyze and simplify the expression

\cot^{-1}\left(\frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} - \sqrt{1-\sin x}}\right)

for

x \in \left(0, \frac{\pi}{2}\right)

.

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hard

Solve for

x

:

\sin^{-1}x + \sin^{-1}(2x) = \frac{\pi}{3}

.

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hard

Calculate the value of

\sin\left(2\tan^{-1}\frac{1}{3}\right) + \cos\left(\tan^{-1}(2\sqrt{2})\right)

.

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hard

Evaluate the validity of the statement: The domain of $\cos^{-1}(3x-4)$ is $[1, 5/3]$ .

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hard

If

\cos^{-1}\left(\frac{x}{a}\right) + \cos^{-1}\left(\frac{y}{b}\right) = \alpha

, demonstrate that

\frac{x^2}{a^2} - \frac{2xy}{ab}\cos\alpha + \frac{y^2}{b^2} = \sin^2\alpha

.

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Inverse Trigonometric FunctionsClass 12 Mathematics Practice Questions