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RD Sharma Solution for Class 11 Science Mathematics Chapter 10 - Sine and Cosine Formulae and Their Applications

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Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 11 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 10 - Sine and Cosine Formulae and Their Applications.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 11 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 11 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

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Exercise/Page

RD Sharma Solution for Class 11 Science Mathematics Chapter 10 - Sine and Cosine Formulae and Their Applications Page/Excercise 10.1

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

Solution 26

Solution 27

Solution 28

Solution 29

Solution 30

C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.

T h e space p e r s o n space i s space o b s e r v i n g space t h e space p e a k space P space f r o m space t h e space p o i n t space Q.
T h e space d i s tan c e space h e space t r a v e l l e d space i s space Q T equals c space m e t r e s space a n d space t h e space a n g l e space o f space i n c l i n a t i o n space o f
Q T space i s space beta.
H e space i s space o b s e r v i n g space t h e space p e a k space f r o m space t h e space p o i n t space a n d space t h e space a n g l e space o f space i n c l i n a t i o n space i s space gamma.
N o w space c o n s i d e r space t h e space t r i a n g l e space capital delta Q U T.
angle T Q U equals beta minus alpha
T h u s comma space sin open parentheses alpha minus beta close parentheses equals a over c
rightwards double arrow a equals c cross times sin open parentheses alpha minus beta close parentheses.... left parenthesis 1 right parenthesis
N o w space c o n s i d e r space t h e space t r i a n g l e space capital delta P Q R.
W e space k n o w space t h a t space angle Q P R equals 90 degree minus alpha
I n space t r i a n g l e space capital delta P T S comma space angle T P S equals 90 degree minus gamma
T h u s comma space angle T P U equals angle Q P R minus angle T P S
rightwards double arrow angle T P U equals open parentheses 90 degree minus alpha close parentheses minus open parentheses 90 degree minus gamma close parentheses
rightwards double arrow angle T P U equals gamma minus alpha
N o w space c o n s i d e r space t h e space capital delta T P U comma
T h u s comma space sin open parentheses gamma minus alpha close parentheses equals a over b
rightwards double arrow b equals fraction numerator a over denominator sin open parentheses gamma minus alpha close parentheses end fraction
S u b s t i t u t i n g space t h e space v a l u e space o f space a space f r o m space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma
b equals fraction numerator c cross times sin open parentheses alpha minus beta close parentheses over denominator sin open parentheses gamma minus alpha close parentheses end fraction... left parenthesis 2 right parenthesis
W e space n e e d space t o space f i n d space t h e space t o t a l space h e i g h t space o f space t h e space p e a k space P R.
H e r e comma space P R equals P S plus S R.... left parenthesis 3 right parenthesis
F r o m space t h e space t r i a n g l e space P S T comma space
sin gamma equals fraction numerator P S over denominator P T end fraction equals fraction numerator P S over denominator b end fraction
rightwards double arrow P S equals b sin gamma.... left parenthesis 4 right parenthesis
F r o m space t h e space t r i a n g l e space Q T W comma space
sin beta equals fraction numerator T W over denominator Q T end fraction equals fraction numerator T W over denominator c end fraction
rightwards double arrow T W equals S R equals c sin beta.... left parenthesis 5 right parenthesis
S u b s t i t u t i n g space t h e space v a l u e s space o f space P S space a n d space S R space f r o m space e q u a t i o n s space left parenthesis 4 right parenthesis space a n d space left parenthesis 5 right parenthesis
i n space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e
P R equals P S plus S R
rightwards double arrow P R equals b sin gamma plus c sin beta
rightwards double arrow P R equals fraction numerator c cross times sin open parentheses alpha minus beta close parentheses over denominator sin open parentheses gamma minus alpha close parentheses end fraction sin gamma plus c sin beta space space space space space space left square bracket f r o m space e q u a t i o n space left parenthesis 2 right parenthesis right square bracket
rightwards double arrow P R equals fraction numerator c cross times sin open parentheses alpha minus beta close parentheses cross times sin gamma plus c sin beta cross times sin open parentheses gamma minus alpha close parentheses over denominator sin open parentheses gamma minus alpha close parentheses end fraction
rightwards double arrow P R equals c open square brackets fraction numerator sin alpha cross times cos beta cross times sin gamma minus cos alpha cross times sin beta cross times sin gamma plus sin beta cross times sin gamma cross times cos alpha minus sin beta cross times sin alpha cross times cos gamma over denominator sin open parentheses gamma minus alpha close parentheses end fraction close square brackets
rightwards double arrow P R equals c open square brackets fraction numerator sin alpha cross times cos beta cross times sin gamma minus sin beta cross times sin alpha cross times cos gamma over denominator sin open parentheses gamma minus alpha close parentheses end fraction close square brackets
rightwards double arrow P R equals fraction numerator c sin alpha cross times open parentheses cos beta cross times sin gamma minus sin beta cross times cos gamma close parentheses over denominator sin open parentheses gamma minus alpha close parentheses end fraction
rightwards double arrow P R equals fraction numerator c sin alpha cross times sin open parentheses gamma minus beta close parentheses over denominator sin open parentheses gamma minus alpha close parentheses end fraction

Solution 31

  

RD Sharma Solution for Class 11 Science Mathematics Chapter 10 - Sine and Cosine Formulae and Their Applications Page/Excercise 10.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

C o n s i d e r space t h e space g i v e n space e q u a t i o n :
cos squared A plus cos squared B plus cos squared C equals 1
rightwards double arrow 1 minus sin squared A plus 1 minus sin squared B plus 1 minus sin squared C equals 1
rightwards double arrow 3 minus sin squared A plus 1 minus sin squared B plus 1 minus sin squared C equals 1

Solution 18

Solution 19

Solution 5

Solution 11

  

RD Sharma Solution for Class 11 Science Mathematics Chapter 10 - Sine and Cosine Formulae and Their Applications Page/Excercise 10VSAQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

B y space cos i n e space r u l e comma space w e space k n o w space t h a t comma
cos A equals fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction ; space cos B equals fraction numerator a squared plus c squared minus b squared over denominator 2 a c end fraction ; space cos C equals fraction numerator a squared plus b squared minus c squared over denominator 2 a b end fraction
T h u s comma space cos A equals fraction numerator 100 plus 144 minus 64 over denominator 2 cross times 10 cross times 12 end fraction equals 3 over 4
a n d
cos C equals fraction numerator 64 plus 100 minus 144 over denominator 2 cross times 8 cross times 10 end fraction equals 1 over 8
space cos A equals 3 over 4
rightwards double arrow A equals cos to the power of minus 1 end exponent open parentheses 3 over 4 close parentheses
rightwards double arrow A almost equal to 41.4096 degree.... left parenthesis 1 right parenthesis
cos C equals 1 over 8
rightwards double arrow C equals cos to the power of minus 1 end exponent open parentheses 1 over 8 close parentheses
rightwards double arrow C almost equal to 82.8192 degree..... left parenthesis 2 right parenthesis
F r o m space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e
C equals 2 A rightwards double arrow lambda equals 2

Solution 7

Solution 8

Solution 9

Solution 10

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 11. Access the CBSE Class 11 Mathematics Chapter 10 - Sine and Cosine Formulae and Their Applications for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 10 - Sine and Cosine Formulae and Their Applications.

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CBSE XI Science - Mathematics

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