Inverse Trigonometric Functions Part - 1

In this course, you will learn the basics of inverse trigonometric functions and how to use them to solve various types of problems. This course is recorded in Hindi for English medium syllabus of Class 12 Mathematics.

The topics covered in this course are:

Derivation of identities: You will learn how to derive some important identities involving inverse trigonometric functions and their properties.

Derivation and explanation of ranges for inverse trigonometric functions: You will learn how to find the principal values and domains of inverse trigonometric functions and how to explain them graphically.

Evaluation type questions: You will learn how to evaluate the values of inverse trigonometric functions for given angles or expressions using the identities and ranges.

Simplification type questions: You will learn how to simplify expressions involving inverse trigonometric functions using the identities and properties.

Solving type questions: You will learn how to solve equations or inequalities involving inverse trigonometric functions using the methods of substitution, squaring or factorization.

The questions in this course are from NCERT Textbook, NCERT exemplar, Board’s Question bank and R.D. Sharma book (private publisher). You will get detailed solutions and explanations for each question along with tips and tricks to save time and avoid mistakes.

This course is suitable for students who want to revise the concepts of inverse trigonometric functions and practice solving different types of problems. It will also help you prepare for your board exams and competitive exams like JEE Main, JEE Advanced, NEET etc.

By the end of this course, you will have a clear understanding of inverse trigonometric functions and their applications. You will also gain confidence and speed in solving problems involving these functions.

6 hours 16 minutes Course Duration
English Syllabus medium
Hindi + English Explanation
Not Logged in Enrollment status
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Course Content

Lecture – 3

00:40:27

Questions Discussed:

Evaluate each of the following:

Question 1. { \displaystyle {{\sin }^{-1}}\left( -\frac{\sqrt{3}}{2} \right) }

Question 2. { \displaystyle {{\cot }^{-1}}\left( \frac{-1}{\sqrt{3}} \right) }

Question 3. { \displaystyle {{\tan }^{-1}}\left( -\frac{1}{\sqrt{3}} \right) }

Question 4. { \displaystyle {{\tan }^{-1}}(1)}+{ \displaystyle{{\cos }^{-1}}\left( -\frac{1}{2} \right)}+{ \displaystyle{{\sin }^{-1}}\left( -\frac{1}{2} \right) }

Question 5. { \displaystyle {{\cos }^{-1}}\left( \frac{1}{2} \right)}+{ \displaystyle2{{\sin }^{-1}}\left( \frac{1}{2} \right) }

Question 6. { \displaystyle {{\tan }^{-1}}\sqrt{3}-{{\sec }^{-1}}(-2) }

Question 7. { \displaystyle {{\sin }^{-1}}\left( \sin \frac{4\pi }{5} \right) }

Question 8. { \displaystyle {{\sin }^{-1}}\left( \sin \frac{2\pi }{3} \right) }

Question 9. { \displaystyle {{\tan }^{-1}}\left( \tan \frac{3\pi }{4} \right) }

Question 10 { \displaystyle {{\cos }^{-1}}\left( \cos \frac{7\pi }{6} \right) }

Question 11 { \displaystyle \sin \left( \frac{\pi }{3}-{{\sin }^{-1}}\left( -\frac{1}{2} \right) \right) }

Question 12 { \displaystyle {{\tan }^{-1}}\sqrt{3}-{{\cot }^{-1}}(-\sqrt{3}) }

Question 13 { \displaystyle {{\csc }^{-1}}(-2) }

Question 14 { \displaystyle {{\sin }^{-1}}\left( \sin \frac{3\pi }{5} \right) }

Question 16 { \displaystyle {{\cos }^{-1}}\left( \cos \frac{13\pi }{6} \right) }

Question 17 { \displaystyle {{\tan }^{-1}}\left( \tan \frac{7\pi }{6} \right) }

Question 18 { \displaystyle {{\cos }^{-1}}[\cos (-680{}^\circ )] }

Question 20 { \displaystyle {{\tan }^{-1}}\left( \tan \frac{5\pi }{6} \right) }