RD SHARMA SOLUTION CHAPTER- 5 Trigonometric Ratios | CLASS 10TH MATHEMATICS-EDUGROWN

Chapter 5 Trigonometric Ratios Exercise Ex. 5.1

Question 1 (i)

Solution 1 (i)

Question 1 (ii)

Solution 1 (ii)

Question 1 (iii)

Solution 1 (iii)

Question 1 (iv)

Solution 1 (iv)

Question 1 (v)

Solution 1 (v)

Question 1 (vi)

Solution 1 (vi)

Question 1 (vii)

Solution 1 (vii)

Question 1 (viii)

Solution 1 (viii)

Question 1 (ix)

Solution 1 (ix)

Question 1 (x)

Solution 1 (x)

Question 1 (xi)

Solution 1 (xi)

Question 1 (xii)

Solution 1 (xii)

Question 2

In ABC right angled at B, AB = 24 cm, BC = 7 cm. Determine

(i)  sin A, cos A
(ii)  sin C, cos C

Solution 2

In ABC by applying Pythagoras theorem
AC² = AB² + BC²
= (24)² + (7)²
= 576 + 49
= 625
AC =  = 25 cm






Question 3

Solution 3

Question 4

Solution 4

Question 5

Given 15 cot A = 8. Find sin A and sec ASolution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36

Solution 36

Question 25

If  find the value of  Solution 25

Given: 

Chapter 5 Trigonometric Ratios Exercise Ex. 5.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26 (i)

Solution 26 (i)

Question 26 (ii)

Solution 26 (ii)

Question 26 (iii)

Solution 26 (iii)

Question 26 (iv)

Solution 26 (iv)

Question 27 (i)

If A = B = 60^o, verify that cos (A – B) = cos A cos B + sin A sin BSolution 27 (i)

Question 27 (ii)

Solution 27 (ii)

Question 27 (iii)

Solution 27 (iii)

Question 28 (i)

Solution 28 (i)

Question 28 (ii)

Solution 28 (ii)

Question 29

Solution 29

Question 30 (i)

Solution 30 (i)

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

If sin (A – B) = sin A cos B – cos A sin B and cos(A – B) = cos A cos B + sin A sin B, find the values of sin 15^o and cos 15^o.Solution 35

Question 36

Solution 36

Question 37

Solution 37

Question 38

Solution 38

Question 39

Solution 39

Question 40

Prove that

Solution 40

Question 30 (ii)

If tan(A + B) = 1 and  0^o < A + B < 90^o, A > B, then find the values of A and B. Solution 30 (ii)

Given: tan(A + B) = 1 and 

Therefore,

A + B = 45^o … (i)

A – B = 30^o … (ii)

Adding the two equations, we get

Chapter 5 Trigonometric Ratios Exercise Ex. 5.3

Question 1

Solution 1

Question 2 (i)

Solution 2 (i)

Question 2 (ii)

Solution 2 (ii)

Question 2 (iii)

Solution 2 (iii)

Question 2 (iv)

Solution 2 (iv)

Question 2 (v)

Solution 2 (v)

Question 2 (vi)

Solution 2 (vi)

Question 2 (vii)

Solution 2 (vii)

Question 2 (viii)

Solution 2 (viii)

Question 2 (ix)

Solution 2 (ix)

Question 2 (x)

Solution 2 (x)

Question 2 (xi)

Solution 2 (xi)

Question 3

Express each one of the following in terms of trigonometric ratios of angles lying between 0^o and 45^o

(i) sin 59^o + cos 56^o

(ii) tan 65^o + cot 49^o

(iii) sec 76^o + cosec 52^o

(iv) cos 78^o + sec 78^o

(v) cosec 54^o + sin 72^o

(vi) cot 85^o + cos 75^o

(vii) sin 67^o + cos 75^oSolution 3

Question 4

Solution 4

Question 5

If sin 3A = cos (A – 26^o), where 3A is an acute angle, find the value of A.Solution 5

Question 6(i)

Solution 6(i)

Question 6(ii)

Solution 6(ii)

Question 7 (i)

Solution 7 (i)

Question 7 (ii)

Solution 7 (ii)

Question 7 (iii)

Solution 7 (iii)

Question 7 (iv)

Solution 7 (iv)

Question 8 (i)

Solution 8 (i)

Question 8 (ii)

Solution 8 (ii)

Question 8 (iii)

Solution 8 (iii)

Question 8 (iv)

Solution 8 (iv)

Question 8 (v)

Solution 8 (v)

Question 9 (i)

Solution 9 (i)

Question 9 (ii)

Solution 9 (ii)

Question 9 (iii)

Solution 9 (iii)

Question 9 (iv)

Solution 9 (iv)

Question 9 (v)

Solution 9 (v)

Question 9 (vi)

Solution 9 (vi)

Question 9 (vii)

Solution 9 (vii)

Question 9 (viii)

Solution 9 (viii)

Question 9 (ix)

Solution 9 (ix)

Question 9 (x)

Solution 9 (x)

Question 10

Solution 10

Question 11 (ii)

If A, B,C are the interior angles of a ΔABC,show that

Solution 11 (ii)

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 6 (iii)

If A, B, C, are the interior angles of a triangle ABC, ∠A = 90^o, then find the value of  Solution 6 (iii)

Given: ∠A = 90^o

For a triangle ABC, ∠A + ∠B + ∠C = 90^o

Question 9 (xi)

Evaluate:  Solution 9 (xi)

Using the identities

Question 11 (i)

If A, B, C are the interior angles of a ∆ABC, show that:  Solution 11 (i)

For a triangle ABC, ∠A + ∠B + ∠C = 90^o

Question 18

If tan 2A = cot(A – 18^o), where 2A is an acute angle, find the value of A.Solution 18

Given: tan 2A = cot(A – 18^o) 

As tan x = cot(90^o – x), we have

cot(90^o – 2A) = cot(A – 18^o)

90^o – 2A = A – 18^o

3A = 108^o

Therefore, A = 36^o.

Chapter 5 Trigonometric Ratios Exercise 5.56

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

So, the correct option is (a).Question 5

Solution 5

Question 6

Solution 6

Chapter 5 Trigonometric Ratios Exercise 5.57

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

So, the correct option is (d).Question 11

Solution 11

So, the correct option is (c).Question 12

Solution 12

Question 13

Solution 13

Question 14

If A and B are complementary angles, then

(a) sin A = sin B

(b) cos A and cos B

(c) tan A = tan B

(d) sec A = cosec BSolution 14

Question 15

Solution 15

So, the correct option is (b).Question 16

Solution 16

So, the correct option is (a).Question 17

Solution 17

So, the correct option is (b).Question 18

Solution 18

So, the correct option is (d).

Chapter 5 Trigonometric Ratios Exercise 5.58

Question 19

Solution 19

Question 20

Solution 20

So, the correct option is (b).Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

So, the correct option is (d).Question 28

Sin 2A = 2 sin A is true when A = 

(a) 0^o

(b) 30^o

(c) 45^o

(d) 60^oSolution 28

So, the correct option is (a).Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Chapter 5 Trigonometric Ratios Exercise 5.59

Question 33

Solution 33

So, the correct option is (c).Question 34

Solution 34

Question 35

Solution 35