Class 11-science RD SHARMA Solutions Maths Chapter 10 - Sine and Cosine Formulae and Their Applications

Ex. 10.1

Ex. 10.2

Ex. 10VSAQ

Sine and Cosine Formulae and Their Applications Exercise Ex. 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

Sine and Cosine Formulae and Their Applications Exercise Ex. 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

Sine and Cosine Formulae and Their Applications Exercise Ex. 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

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Class 11-science RD SHARMA Solutions Maths Chapter 10 - Sine and Cosine Formulae and Their Applications

Sine and Cosine Formulae and Their Applications Exercise Ex. 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

Solution 31

Sine and Cosine Formulae and Their Applications Exercise Ex. 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

Solution 18

Solution 19

Solution 5

Solution 11

Sine and Cosine Formulae and Their Applications Exercise Ex. 10VSAQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

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