JEE Exam > JEE Notes > Mathematics (Maths) Class 12 > RD Sharma Class 12 Solutions - Inverse Trigonometric Functions
RD Sharma Class 12 Solutions - Inverse Trigonometric Functions | Mathematics (Maths) Class 12 - JEE PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1 4. Inverse Trigonometric Functions Exercise 4.1 1 A. Question Find the principal value of each of the following: Answer Let Then sin y = We know that the principal value of is Therefore the principal value of is 1 B. Question Find the principal value of each of the following: Answer Let cos y = We need to find the value of y. We know that the value of cos is negative for the second quadrant and hence the value lies in [0, p]. cos y = – cos cos y = y = 1 C. Question Find the principal value of each of the following: Answer Page 2 4. Inverse Trigonometric Functions Exercise 4.1 1 A. Question Find the principal value of each of the following: Answer Let Then sin y = We know that the principal value of is Therefore the principal value of is 1 B. Question Find the principal value of each of the following: Answer Let cos y = We need to find the value of y. We know that the value of cos is negative for the second quadrant and hence the value lies in [0, p]. cos y = – cos cos y = y = 1 C. Question Find the principal value of each of the following: Answer 1 D. Question Find the principal value of each of the following: Answer 1 E. Question Find the principal value of each of the following: Answer Let Then Page 3 4. Inverse Trigonometric Functions Exercise 4.1 1 A. Question Find the principal value of each of the following: Answer Let Then sin y = We know that the principal value of is Therefore the principal value of is 1 B. Question Find the principal value of each of the following: Answer Let cos y = We need to find the value of y. We know that the value of cos is negative for the second quadrant and hence the value lies in [0, p]. cos y = – cos cos y = y = 1 C. Question Find the principal value of each of the following: Answer 1 D. Question Find the principal value of each of the following: Answer 1 E. Question Find the principal value of each of the following: Answer Let Then We know that the principal value of is Therefore the principal value of is . 1 F. Question Find the principal value of each of the following: Answer Let y = Therefore, sin y = We know that the principal value of is And Therefore the principal value of is . 2 A. Question Find the principal value of each of the following: Answer 2 B. Question Find the principal value of each of the following: Answer Page 4 4. Inverse Trigonometric Functions Exercise 4.1 1 A. Question Find the principal value of each of the following: Answer Let Then sin y = We know that the principal value of is Therefore the principal value of is 1 B. Question Find the principal value of each of the following: Answer Let cos y = We need to find the value of y. We know that the value of cos is negative for the second quadrant and hence the value lies in [0, p]. cos y = – cos cos y = y = 1 C. Question Find the principal value of each of the following: Answer 1 D. Question Find the principal value of each of the following: Answer 1 E. Question Find the principal value of each of the following: Answer Let Then We know that the principal value of is Therefore the principal value of is . 1 F. Question Find the principal value of each of the following: Answer Let y = Therefore, sin y = We know that the principal value of is And Therefore the principal value of is . 2 A. Question Find the principal value of each of the following: Answer 2 B. Question Find the principal value of each of the following: Answer 3 A. Question Find the domain of each of the following functions: f(x) = sin –1 x 2 Answer Domain of lies in the interval [–1, 1]. Therefore domain of lies in the interval [–1, 1]. –1 1 But cannot take negative values, So, 0 1 –1 1 Hence domain of is [–1, 1]. 3 B. Question Find the domain of each of the following functions: f(x) = sin –1 x + sinx Answer Domain of lies in the interval [–1, 1]. –1 1. The domain of sin x lies in the interval –1.57 1.57 From the above we can see that the domain of sin –1 x + sinx is the intersection of the domains of sin –1 x and sin x. So domain of sin –1 x + sinx is [–1, 1]. 3 C. Question Find the domain of each of the following functions: f(x) = Answer Domain of lies in the interval [–1, 1]. Therefore, Domain of lies in the interval [–1, 1]. –1 1 Page 5 4. Inverse Trigonometric Functions Exercise 4.1 1 A. Question Find the principal value of each of the following: Answer Let Then sin y = We know that the principal value of is Therefore the principal value of is 1 B. Question Find the principal value of each of the following: Answer Let cos y = We need to find the value of y. We know that the value of cos is negative for the second quadrant and hence the value lies in [0, p]. cos y = – cos cos y = y = 1 C. Question Find the principal value of each of the following: Answer 1 D. Question Find the principal value of each of the following: Answer 1 E. Question Find the principal value of each of the following: Answer Let Then We know that the principal value of is Therefore the principal value of is . 1 F. Question Find the principal value of each of the following: Answer Let y = Therefore, sin y = We know that the principal value of is And Therefore the principal value of is . 2 A. Question Find the principal value of each of the following: Answer 2 B. Question Find the principal value of each of the following: Answer 3 A. Question Find the domain of each of the following functions: f(x) = sin –1 x 2 Answer Domain of lies in the interval [–1, 1]. Therefore domain of lies in the interval [–1, 1]. –1 1 But cannot take negative values, So, 0 1 –1 1 Hence domain of is [–1, 1]. 3 B. Question Find the domain of each of the following functions: f(x) = sin –1 x + sinx Answer Domain of lies in the interval [–1, 1]. –1 1. The domain of sin x lies in the interval –1.57 1.57 From the above we can see that the domain of sin –1 x + sinx is the intersection of the domains of sin –1 x and sin x. So domain of sin –1 x + sinx is [–1, 1]. 3 C. Question Find the domain of each of the following functions: f(x) = Answer Domain of lies in the interval [–1, 1]. Therefore, Domain of lies in the interval [–1, 1]. –1 1 0 1 1 2 and Domain of is [– [1, . 3 D. Question Find the domain of each of the following functions: f(x) = sin –1 x + sin –1 2x Answer Domain of lies in the interval [–1, 1]. –1 1 Therefore, the domain of lies in the interval –1 1 The domain of sin –1 x + sin –1 2x is the intersection of the domains of sin –1 x and sin –1 2x. So, Domain of sin –1 x + sin –1 2x is . 4. Question If sin –1 x + sin –1 y + sin –1 z + sin –1 t = 2p, then find the value of x 2 + y 2 + z 2 + t 2 . Answer Range of sin –1 x is . Give that sin –1 x + sin –1 y + sin –1 z + sin –1 t = 2p Each of sin –1 x, sin –1 y, sin –1 z, sin –1 t takes value of . So, x = 1, y = 1, z = 1 and t = 1. Hence, = x 2 + y 2 + z 2 + t 2 = 1 + 1 + 1 + 1 = 4 5. Question If (sin –1 x) 2 + (sin –1 y) 2 + (sin –1 z) 2 = 3/4 p 2 . Find x 2 + y 2 + z 2 . AnswerRead More
|
204 videos|290 docs|139 tests
|
About this Document
|
4.76/5 Rating |
|
Dec 22, 2024 Last updated |
Document Description: RD Sharma Class 12 Solutions - Inverse Trigonometric Functions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation.
The notes and questions for RD Sharma Class 12 Solutions - Inverse Trigonometric Functions have been prepared according to the JEE exam syllabus. Information about RD Sharma Class 12 Solutions - Inverse Trigonometric Functions covers topics
like and RD Sharma Class 12 Solutions - Inverse Trigonometric Functions Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Class 12 Solutions - Inverse Trigonometric Functions.
Introduction of RD Sharma Class 12 Solutions - Inverse Trigonometric Functions in English is available as part of our Mathematics (Maths) Class 12
for JEE & RD Sharma Class 12 Solutions - Inverse Trigonometric Functions in Hindi for Mathematics (Maths) Class 12 course.
Download more important topics related with notes, lectures and mock test series for JEE
Exam by signing up for free. JEE: RD Sharma Class 12 Solutions - Inverse Trigonometric Functions | Mathematics (Maths) Class 12 - JEE
Description
Full syllabus notes, lecture & questions for RD Sharma Class 12 Solutions - Inverse Trigonometric Functions | Mathematics (Maths) Class 12 - JEE - JEE | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 12 | Best notes, free PDF download
Information about RD Sharma Class 12 Solutions - Inverse Trigonometric Functions
In this doc you can find the meaning of RD Sharma Class 12 Solutions - Inverse Trigonometric Functions defined & explained in the simplest way possible. Besides explaining types of
RD Sharma Class 12 Solutions - Inverse Trigonometric Functions theory, EduRev gives you an ample number of questions to practice RD Sharma Class 12 Solutions - Inverse Trigonometric Functions tests, examples and also practice JEE
tests
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Summary
,RD Sharma Class 12 Solutions - Inverse Trigonometric Functions | Mathematics (Maths) Class 12 - JEE
,video lectures
,practice quizzes
,Extra Questions
,mock tests for examination
,Free
,Sample Paper
,study material
,Previous Year Questions with Solutions
,shortcuts and tricks
,Exam
,RD Sharma Class 12 Solutions - Inverse Trigonometric Functions | Mathematics (Maths) Class 12 - JEE
,MCQs
,Semester Notes
,past year papers
,Objective type Questions
,ppt
,RD Sharma Class 12 Solutions - Inverse Trigonometric Functions | Mathematics (Maths) Class 12 - JEE
,Important questions
,Viva Questions
;
Additional Information about RD Sharma Class 12 Solutions - Inverse Trigonometric Functions for JEE Preparation
RD Sharma Class 12 Solutions - Inverse Trigonometric Functions Free PDF Download
The RD Sharma Class 12 Solutions - Inverse Trigonometric Functions is an invaluable resource that delves deep into the core of the JEE exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the RD Sharma Class 12 Solutions - Inverse Trigonometric Functions now and kickstart your journey towards success in the JEE exam.
Importance of RD Sharma Class 12 Solutions - Inverse Trigonometric Functions
The importance of RD Sharma Class 12 Solutions - Inverse Trigonometric Functions cannot be overstated, especially for JEE aspirants.
This document holds the key to success in the JEE exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
RD Sharma Class 12 Solutions - Inverse Trigonometric Functions Notes
RD Sharma Class 12 Solutions - Inverse Trigonometric Functions Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to RD Sharma Class 12 Solutions - Inverse Trigonometric Functions.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, RD Sharma Class 12 Solutions - Inverse Trigonometric Functions Notes on EduRev are your ultimate resource for success.
RD Sharma Class 12 Solutions - Inverse Trigonometric Functions JEE Questions
The "RD Sharma Class 12 Solutions - Inverse Trigonometric Functions JEE Questions" guide is a valuable resource for all aspiring students preparing for the
JEE exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study RD Sharma Class 12 Solutions - Inverse Trigonometric Functions on the App
Students of JEE can study RD Sharma Class 12 Solutions - Inverse Trigonometric Functions alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the RD Sharma Class 12 Solutions - Inverse Trigonometric Functions,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of RD Sharma Class 12 Solutions - Inverse Trigonometric Functions is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup