Open App

Commerce Exam > Commerce Notes > Mathematics (Maths) Class 11 > RD Sharma Class 11 Solutions Chapter - Trigonometric Functions

RD Sharma Class 11 Solutions Chapter - Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce PDF Download

Download, print and study this document offline

Please wait while the PDF view is loading

 Page 1


5. Trigonometric Functions
Exercise 5.1
1. Question
Prove the following identities
sec
4
x – sec
2
x = tan
4
x + tan
2
x
Answer
LHS = sec
4
x – sec
2
x
= (sec
2
x) 
2
 – sec
2
x
We know sec
2
 ? = 1 + tan
2
 ?.
= (1 + tan
2
x) 
2
 – (1 + tan
2
x)
= 1 + 2tan
2
x + tan
4
x – 1 - tan
2
x
= tan
4
x + tan
2
x = RHS
Hence proved.
2. Question
Prove the following identities
sin
6
x + cos
6
x = 1 – 3 sin
2
x cos
2
x
Answer
LHS = sin
6
x + cos
6
x
= (sin
2
x)
3
 + (cos
2
x)
3
We know that a
3
 + b
3
 = (a + b) (a
2
 + b
2
 – ab)
= (sin
2
x + cos
2
x) [(sin
2
x)
2
 + (cos
2
x)
2
 – sin
2
x cos
2
x]
We know that sin
2
x + cos
2
x = 1 and a
2
 + b
2
 = (a + b)
2
 – 2ab
= 1 × [(sin
2
x + cos
2
x)
2
 – 2sin
2
x cos
2
x – sin
2
x cos
2
x
= 1
2
 - 3sin
2
x cos
2
x
= 1 - 3sin
2
x cos
2
x = RHS
Hence proved.
3. Question
Prove the following identities
(cosecx – sinx) (secx – cosx) (tanx + cotx) = 1
Answer
LHS = (cosecx – sinx) (secx – cosx) (tanx + cotx)
We know that 
Page 2


5. Trigonometric Functions
Exercise 5.1
1. Question
Prove the following identities
sec
4
x – sec
2
x = tan
4
x + tan
2
x
Answer
LHS = sec
4
x – sec
2
x
= (sec
2
x) 
2
 – sec
2
x
We know sec
2
 ? = 1 + tan
2
 ?.
= (1 + tan
2
x) 
2
 – (1 + tan
2
x)
= 1 + 2tan
2
x + tan
4
x – 1 - tan
2
x
= tan
4
x + tan
2
x = RHS
Hence proved.
2. Question
Prove the following identities
sin
6
x + cos
6
x = 1 – 3 sin
2
x cos
2
x
Answer
LHS = sin
6
x + cos
6
x
= (sin
2
x)
3
 + (cos
2
x)
3
We know that a
3
 + b
3
 = (a + b) (a
2
 + b
2
 – ab)
= (sin
2
x + cos
2
x) [(sin
2
x)
2
 + (cos
2
x)
2
 – sin
2
x cos
2
x]
We know that sin
2
x + cos
2
x = 1 and a
2
 + b
2
 = (a + b)
2
 – 2ab
= 1 × [(sin
2
x + cos
2
x)
2
 – 2sin
2
x cos
2
x – sin
2
x cos
2
x
= 1
2
 - 3sin
2
x cos
2
x
= 1 - 3sin
2
x cos
2
x = RHS
Hence proved.
3. Question
Prove the following identities
(cosecx – sinx) (secx – cosx) (tanx + cotx) = 1
Answer
LHS = (cosecx – sinx) (secx – cosx) (tanx + cotx)
We know that 
We know that sin
2
x + cos
2
x = 1.
= 1 = RHS
Hence proved.
4. Question
Prove the following identities
cosecx (secx – 1) – cotx (1 – cosx) = tanx – sinx
Answer
LHS = cosecx (secx – 1) – cotx (1 – cosx)
We know that 
We know that 1 – cos
2
x = sin
2
x.
= RHS
Hence proved.
5. Question
Prove the following identities
Answer
LHS 
We know that 
Page 3


5. Trigonometric Functions
Exercise 5.1
1. Question
Prove the following identities
sec
4
x – sec
2
x = tan
4
x + tan
2
x
Answer
LHS = sec
4
x – sec
2
x
= (sec
2
x) 
2
 – sec
2
x
We know sec
2
 ? = 1 + tan
2
 ?.
= (1 + tan
2
x) 
2
 – (1 + tan
2
x)
= 1 + 2tan
2
x + tan
4
x – 1 - tan
2
x
= tan
4
x + tan
2
x = RHS
Hence proved.
2. Question
Prove the following identities
sin
6
x + cos
6
x = 1 – 3 sin
2
x cos
2
x
Answer
LHS = sin
6
x + cos
6
x
= (sin
2
x)
3
 + (cos
2
x)
3
We know that a
3
 + b
3
 = (a + b) (a
2
 + b
2
 – ab)
= (sin
2
x + cos
2
x) [(sin
2
x)
2
 + (cos
2
x)
2
 – sin
2
x cos
2
x]
We know that sin
2
x + cos
2
x = 1 and a
2
 + b
2
 = (a + b)
2
 – 2ab
= 1 × [(sin
2
x + cos
2
x)
2
 – 2sin
2
x cos
2
x – sin
2
x cos
2
x
= 1
2
 - 3sin
2
x cos
2
x
= 1 - 3sin
2
x cos
2
x = RHS
Hence proved.
3. Question
Prove the following identities
(cosecx – sinx) (secx – cosx) (tanx + cotx) = 1
Answer
LHS = (cosecx – sinx) (secx – cosx) (tanx + cotx)
We know that 
We know that sin
2
x + cos
2
x = 1.
= 1 = RHS
Hence proved.
4. Question
Prove the following identities
cosecx (secx – 1) – cotx (1 – cosx) = tanx – sinx
Answer
LHS = cosecx (secx – 1) – cotx (1 – cosx)
We know that 
We know that 1 – cos
2
x = sin
2
x.
= RHS
Hence proved.
5. Question
Prove the following identities
Answer
LHS 
We know that 
We know that a
3
 + b
3
 = (a + b) (a
2
 + b
2
 – ab)
We know that sin
2
x + cos
2
x = 1.
= sinx
= RHS
Hence proved.
6. Question
Prove the following identities
 = (secx cosecx + 1)
Answer
LHS 
We know that 
We know that a
3
 - b
3
 = (a - b) (a
2
 + b
2
 + ab)
We know that sin
2
x + cos
2
x = 1.
Page 4


5. Trigonometric Functions
Exercise 5.1
1. Question
Prove the following identities
sec
4
x – sec
2
x = tan
4
x + tan
2
x
Answer
LHS = sec
4
x – sec
2
x
= (sec
2
x) 
2
 – sec
2
x
We know sec
2
 ? = 1 + tan
2
 ?.
= (1 + tan
2
x) 
2
 – (1 + tan
2
x)
= 1 + 2tan
2
x + tan
4
x – 1 - tan
2
x
= tan
4
x + tan
2
x = RHS
Hence proved.
2. Question
Prove the following identities
sin
6
x + cos
6
x = 1 – 3 sin
2
x cos
2
x
Answer
LHS = sin
6
x + cos
6
x
= (sin
2
x)
3
 + (cos
2
x)
3
We know that a
3
 + b
3
 = (a + b) (a
2
 + b
2
 – ab)
= (sin
2
x + cos
2
x) [(sin
2
x)
2
 + (cos
2
x)
2
 – sin
2
x cos
2
x]
We know that sin
2
x + cos
2
x = 1 and a
2
 + b
2
 = (a + b)
2
 – 2ab
= 1 × [(sin
2
x + cos
2
x)
2
 – 2sin
2
x cos
2
x – sin
2
x cos
2
x
= 1
2
 - 3sin
2
x cos
2
x
= 1 - 3sin
2
x cos
2
x = RHS
Hence proved.
3. Question
Prove the following identities
(cosecx – sinx) (secx – cosx) (tanx + cotx) = 1
Answer
LHS = (cosecx – sinx) (secx – cosx) (tanx + cotx)
We know that 
We know that sin
2
x + cos
2
x = 1.
= 1 = RHS
Hence proved.
4. Question
Prove the following identities
cosecx (secx – 1) – cotx (1 – cosx) = tanx – sinx
Answer
LHS = cosecx (secx – 1) – cotx (1 – cosx)
We know that 
We know that 1 – cos
2
x = sin
2
x.
= RHS
Hence proved.
5. Question
Prove the following identities
Answer
LHS 
We know that 
We know that a
3
 + b
3
 = (a + b) (a
2
 + b
2
 – ab)
We know that sin
2
x + cos
2
x = 1.
= sinx
= RHS
Hence proved.
6. Question
Prove the following identities
 = (secx cosecx + 1)
Answer
LHS 
We know that 
We know that a
3
 - b
3
 = (a - b) (a
2
 + b
2
 + ab)
We know that sin
2
x + cos
2
x = 1.
We know that 
= cosecx × secx + 1
= secx cosecx + 1
= RHS
Hence proved.
7. Question
Prove the following identities
Answer
LHS 
We know that a
3
 ± b
3
 = (a ± b) (a
2
 + b
2
± ab)
We know that sin
2
x + cos
2
x = 1.
= 1 - sinx cosx + 1 + sinx cosx
= 2
= RHS
Hence proved.
8. Question
Prove the following identities
(secx sec y + tanx tan y)
2
 – (secx tan y + tanx sec y)
2
 = 1
Answer
LHS = (secx sec y + tanx tan y)
2
 – (secx tan y + tanx sec y)
2
= [(secx sec y)
2
 + (tanx tan y)
2
 + 2 (secx sec y) (tanx tan y)] – [(secx tan y)
2
 + (tanx sec y)
2
 + 2 (secx tan y)
(tanx sec y)]
= [sec
2
x sec
2
 y + tan
2
x tan
2
 y + 2 (secx sec y) (tanx tan y)] – [sec
2
x tan
2
 y + tan
2
x sec
2
 y + 2 (sec
2
x tan
2
 y)
(tanx sec y)]
= sec
2
x sec
2
 y - sec
2
x tan
2
 y + tan
2
x tan
2
 y - tan
2
x sec
2
 y
= sec
2
x (sec
2
 y - tan
2
 y) + tan
2
x (tan
2
 y - sec
2
 y)
= sec
2
x (sec
2
 y - tan
2
 y) - tan
2
x (sec
2
 y - tan
2
 y)
We know that sec
2
x – tan
2
x = 1.
= sec
2
x × 1 – tan
2
x × 1
= sec
2
x – tan
2
x
= 1
Page 5


5. Trigonometric Functions
Exercise 5.1
1. Question
Prove the following identities
sec
4
x – sec
2
x = tan
4
x + tan
2
x
Answer
LHS = sec
4
x – sec
2
x
= (sec
2
x) 
2
 – sec
2
x
We know sec
2
 ? = 1 + tan
2
 ?.
= (1 + tan
2
x) 
2
 – (1 + tan
2
x)
= 1 + 2tan
2
x + tan
4
x – 1 - tan
2
x
= tan
4
x + tan
2
x = RHS
Hence proved.
2. Question
Prove the following identities
sin
6
x + cos
6
x = 1 – 3 sin
2
x cos
2
x
Answer
LHS = sin
6
x + cos
6
x
= (sin
2
x)
3
 + (cos
2
x)
3
We know that a
3
 + b
3
 = (a + b) (a
2
 + b
2
 – ab)
= (sin
2
x + cos
2
x) [(sin
2
x)
2
 + (cos
2
x)
2
 – sin
2
x cos
2
x]
We know that sin
2
x + cos
2
x = 1 and a
2
 + b
2
 = (a + b)
2
 – 2ab
= 1 × [(sin
2
x + cos
2
x)
2
 – 2sin
2
x cos
2
x – sin
2
x cos
2
x
= 1
2
 - 3sin
2
x cos
2
x
= 1 - 3sin
2
x cos
2
x = RHS
Hence proved.
3. Question
Prove the following identities
(cosecx – sinx) (secx – cosx) (tanx + cotx) = 1
Answer
LHS = (cosecx – sinx) (secx – cosx) (tanx + cotx)
We know that 
We know that sin
2
x + cos
2
x = 1.
= 1 = RHS
Hence proved.
4. Question
Prove the following identities
cosecx (secx – 1) – cotx (1 – cosx) = tanx – sinx
Answer
LHS = cosecx (secx – 1) – cotx (1 – cosx)
We know that 
We know that 1 – cos
2
x = sin
2
x.
= RHS
Hence proved.
5. Question
Prove the following identities
Answer
LHS 
We know that 
We know that a
3
 + b
3
 = (a + b) (a
2
 + b
2
 – ab)
We know that sin
2
x + cos
2
x = 1.
= sinx
= RHS
Hence proved.
6. Question
Prove the following identities
 = (secx cosecx + 1)
Answer
LHS 
We know that 
We know that a
3
 - b
3
 = (a - b) (a
2
 + b
2
 + ab)
We know that sin
2
x + cos
2
x = 1.
We know that 
= cosecx × secx + 1
= secx cosecx + 1
= RHS
Hence proved.
7. Question
Prove the following identities
Answer
LHS 
We know that a
3
 ± b
3
 = (a ± b) (a
2
 + b
2
± ab)
We know that sin
2
x + cos
2
x = 1.
= 1 - sinx cosx + 1 + sinx cosx
= 2
= RHS
Hence proved.
8. Question
Prove the following identities
(secx sec y + tanx tan y)
2
 – (secx tan y + tanx sec y)
2
 = 1
Answer
LHS = (secx sec y + tanx tan y)
2
 – (secx tan y + tanx sec y)
2
= [(secx sec y)
2
 + (tanx tan y)
2
 + 2 (secx sec y) (tanx tan y)] – [(secx tan y)
2
 + (tanx sec y)
2
 + 2 (secx tan y)
(tanx sec y)]
= [sec
2
x sec
2
 y + tan
2
x tan
2
 y + 2 (secx sec y) (tanx tan y)] – [sec
2
x tan
2
 y + tan
2
x sec
2
 y + 2 (sec
2
x tan
2
 y)
(tanx sec y)]
= sec
2
x sec
2
 y - sec
2
x tan
2
 y + tan
2
x tan
2
 y - tan
2
x sec
2
 y
= sec
2
x (sec
2
 y - tan
2
 y) + tan
2
x (tan
2
 y - sec
2
 y)
= sec
2
x (sec
2
 y - tan
2
 y) - tan
2
x (sec
2
 y - tan
2
 y)
We know that sec
2
x – tan
2
x = 1.
= sec
2
x × 1 – tan
2
x × 1
= sec
2
x – tan
2
x
= 1
= RHS
Hence proved.
9. Question
Prove the following identities
Answer
RHS 
We know that sin
2
x + cos
2
x = 1.
We know that 1 – cos
2
x = sin
2
x.
We know that 1 – sin
2
x = cos
2
x.

	Mathematics (Maths) Class 11 75 videos\|238 docs\|91 tests

Mathematics (Maths) Class 11

75 videos|238 docs|91 tests

Join Course for Free

Top Courses for Commerce

View all

Related Exams

Commerce Humanities/Arts JEE Class 11 Class 12 Grade 11

About this Document

	4.86/5 Rating
	Nov 21, 2024 Last updated

Document Description: RD Sharma Class 11 Solutions Chapter - Trigonometric Functions for Commerce 2024 is part of Mathematics (Maths) Class 11 preparation. The notes and questions for RD Sharma Class 11 Solutions Chapter - Trigonometric Functions have been prepared according to the Commerce exam syllabus. Information about RD Sharma Class 11 Solutions Chapter - Trigonometric Functions covers topics like and RD Sharma Class 11 Solutions Chapter - Trigonometric Functions Example, for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Class 11 Solutions Chapter - Trigonometric Functions.

Introduction of RD Sharma Class 11 Solutions Chapter - Trigonometric Functions in English is available as part of our Mathematics (Maths) Class 11 for Commerce & RD Sharma Class 11 Solutions Chapter - Trigonometric Functions in Hindi for Mathematics (Maths) Class 11 course. Download more important topics related with notes, lectures and mock test series for Commerce Exam by signing up for free. Commerce: RD Sharma Class 11 Solutions Chapter - Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

Description

Full syllabus notes, lecture & questions for RD Sharma Class 11 Solutions Chapter - Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce - Commerce | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 11 | Best notes, free PDF download

Information about RD Sharma Class 11 Solutions Chapter - Trigonometric Functions

In this doc you can find the meaning of RD Sharma Class 11 Solutions Chapter - Trigonometric Functions defined & explained in the simplest way possible. Besides explaining types of RD Sharma Class 11 Solutions Chapter - Trigonometric Functions theory, EduRev gives you an ample number of questions to practice RD Sharma Class 11 Solutions Chapter - Trigonometric Functions tests, examples and also practice Commerce tests

	Mathematics (Maths) Class 11 75 videos\|238 docs\|91 tests

Mathematics (Maths) Class 11

75 videos|238 docs|91 tests

Join Course for Free

Download as PDF

Explore Courses for Commerce exam

Top Courses for Commerce

Explore Courses

Signup for Free!

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.

Start learning for Free

10M+ students study on EduRev

Semester Notes

mock tests for examination

RD Sharma Class 11 Solutions Chapter - Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

pdf

Viva Questions

Exam

MCQs

shortcuts and tricks

ppt

Important questions

Sample Paper

RD Sharma Class 11 Solutions Chapter - Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce

study material

video lectures

Free

Previous Year Questions with Solutions

Extra Questions

Summary

practice quizzes

Objective type Questions

past year papers

;

Additional Information about RD Sharma Class 11 Solutions Chapter - Trigonometric Functions for Commerce Preparation

RD Sharma Class 11 Solutions Chapter - Trigonometric Functions Free PDF Download

The RD Sharma Class 11 Solutions Chapter - Trigonometric Functions is an invaluable resource that delves deep into the core of the Commerce 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 11 Solutions Chapter - Trigonometric Functions now and kickstart your journey towards success in the Commerce exam.

Importance of RD Sharma Class 11 Solutions Chapter - Trigonometric Functions

The importance of RD Sharma Class 11 Solutions Chapter - Trigonometric Functions cannot be overstated, especially for Commerce aspirants. This document holds the key to success in the Commerce 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 11 Solutions Chapter - Trigonometric Functions Notes

RD Sharma Class 11 Solutions Chapter - 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 11 Solutions Chapter - 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 11 Solutions Chapter - Trigonometric Functions Notes on EduRev are your ultimate resource for success.

RD Sharma Class 11 Solutions Chapter - Trigonometric Functions Commerce Questions

The "RD Sharma Class 11 Solutions Chapter - Trigonometric Functions Commerce Questions" guide is a valuable resource for all aspiring students preparing for the Commerce 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 11 Solutions Chapter - Trigonometric Functions on the App

Students of Commerce can study RD Sharma Class 11 Solutions Chapter - Trigonometric Functions alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the RD Sharma Class 11 Solutions Chapter - 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 11 Solutions Chapter - Trigonometric Functions is prepared as per the latest Commerce syllabus.

Education Revolution