RD SHARMA SOLUTION CHAPTER- 6 Trigonometric Identities | CLASS 10TH MATHEMATICS-EDUGROWN

Chapter 6 Trigonometric Identities Exercise Ex. 6.1

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(i)

Solution 23(i)

Question 23(ii)

Solution 23(ii)

Question 24

Solution 24

Question 25

Solution 25

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 37. i

Solution 37. i

Question 37. ii

Prove the following trigonometric identities:

Solution 37. ii

L.H.S.,

Question 38(i)

Solution 38(i)

Question 38(ii)

Solution 38(ii)

Question 38(iii)

Solution 38(iii)

Question 38(iv)

Solution 38(iv)

Question 39

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

Solution 46

Question 47 (i)

Solution 47 (i)

Question 47 (ii)

Solution 47 (ii)

Question 47 (iii)

Solution 47 (iii)

Question 47(iv)

Prove that:

(sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θSolution 47(iv)

Question 48

Solution 48

Question 49

Solution 49

Question 50

Prove that:

Solution 50

Question 51

Solution 51

Question 52

Solution 52

Question 53

Solution 53

Question 54

Solution 54

Question 55. i

Solution 55. i

Question 55. ii

Solution 55. ii

Question 56

Solution 56

Question 57

Solution 57

Question 58

Solution 58

Question 59

Solution 59

Question 60

Solution 60

Question 61

Solution 61

Question 62

Solution 62

Question 63

Solution 63

Question 64

Solution 64

Question 65. i

Solution 65. i

Question 65(ii)

Solution 65(ii)

Question 66

Solution 66

Question 67

Solution 67

Question 68

Solution 68

Question 69

Solution 69

Question 70

Solution 70

Question 71

Solution 71

Question 72

Solution 72

Question 73

Solution 73

Question 74

Solution 74

Question 75

Solution 75

Question 76

Solution 76

Question 77

Solution 77

Question 78

Solution 78

Question 79

Solution 79

Question 80

Solution 80

Question 81

Solution 81

Question 82

Solution 82

Question 83

Solution 83

Question 84

Solution 84

Question 85

Solution 85

Question 86

If sin θ + 2 cos θ = 1 prove that 2 sin θ – cos θ = 2.Solution 86

Question 23 (iii)

Solution 23 (iii)

To prove: 

Consider LHS

= RHS

Hence, proved.

Chapter 6 Trigonometric Identities Exercise Ex. 6.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

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

If 2sin² θ – cos² θ = 2, then find the value of θ.Solution 13

Question 14

If tan θ – 1 = 0, find the value of sin²θ – cos² θ.Solution 14

Question 4

If  evaluate  Solution 4

Given: 

Consider,

 … [Multiplying and dividing by tan θ]

Chapter 6 Trigonometric Identities Exercise 6.56

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

sec⁴ – sec²A  is equal to

(a)  tan²A –  tan⁴A     (b) tan⁴A –  tan²A 

(c) tan⁴A + tan²A      (d) tan²A –  tan⁴A  Solution 5

Question 6

cos⁴A-sin⁴A is equal  to

(a)  2cos²A+1    (b) 2cos²A-1   

(c)  2sin²A-1     (d) 2sin²A+1  Solution 6

Chapter 6 Trigonometric Identities Exercise 6.57

Question 7

Solution 7

Question 8

Solution 8

Question 9

The value of (1+cotθ – cosecθ )  (1+tanθ + secθ) is

 (a) 1     (b) 2      (c) 4      (d) 0Solution 9

Question 10

Solution 10

Question 11

(cosecθ – sinθ) (secθ – cosθ) (tanθ + cotθ) is equal

(a) 0          (b)   1       (c)-1        (d) None of theeSolution 11

Question 12

Solution 12

Question 13

If  x =a secθ  and  y=b tanθ  then  b²x²a²y²=

(a) ab      (b) a² – b²       (c) a² + b²    (d) a²b²Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

If acosθ + bsinθ = 4 and asinθ-bcosθ = 3, then a²+b²=

(a) 7    (b) 12      (c) 25      (d) None of theseSolution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Chapter 6 Trigonometric Identities Exercise 6.58

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

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

If sin θ – cos θ = 0, then the value of sin⁴ θ + cos⁴ θ is

1. 1
2. 
3. 
4. 

Solution 29

Question 30

The value of sin (45° + θ) – cos (45° – θ) is equal to

1. 2 cos θ
2. 0
3. 2 sin θ
4. 1

Solution 30

Question 31

If ΔABC is right angled at C, then the value of cos (A + B) is

1. 0
2. 1
3. 
4. 

Solution 31

Chapter 6 Trigonometric Identities Exercise 6.59

Question 32

If cos 8θ = sin θ and 8θ < 90°, then the value of tan 6θ is

1. 
2. 
3. 1
4. 0

Solution 32

Question 33

If cos (α + β) = 0, then sin (α  –  β) can be reduced to

1. cos β
2. cos 2β
3. sin α
4. sin 2α

Solution 33