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NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4

December 26, 2018 by Dattu

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 8 Introduction to Trigonometry Class 10 NCERT Solutions Ex 8.4.

  • Introduction to Trigonometry Class 10 Ex 8.1
  • Introduction to Trigonometry Class 10 Ex 8.2
  • Introduction to Trigonometry Class 10 Ex 8.3
BoardCBSE
TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 8
Chapter NameIntroduction to Trigonometry
ExerciseEx 8.4
Number of Questions Solved5
CategoryNCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4

NCERT Solutions for Class 10 Maths

Page No : 193

Question 1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 23

Question 2. Write all the other trigonometric ratios of ∠A in terms of sec A.

Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 24

Question 3. Evaluate :
(i) \(\frac { { sin }^{ 2 }{ 63 }^{ 0 }+{ sin }^{ 2 }{ 27 }^{ 0 } }{ { cos }^{ 2 }{ 17 }^{ 0 }+{ cos }^{ 2 }{ 73 }^{ 0 } } \)
(ii) sin 25° cos 65° + cos 25° sin 65°

Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 25

Question 4. Choose the correct option. Justify your choice.
(i) 9 sec2A – 9 tan2A =
(A) 1 (B) 9 (C) 8 (D) 0

(ii) (1 + tan θ + sec θ) (1 + cot θ – cosec θ)
(A) 0 (B) 1 (C) 2 (D) – 1

(iii) (secA + tanA) (1 – sinA) =
(A) secA (B) sinA (C) cosecA (D) cosA

(iv) \(\frac { 1+{ tan }^{ 2 }A }{ 1+{ cot }^{ 2 }A } =\)
(A) sec2A (B) -1 (C) cot2A (D) tan2A

Solution:
(i) 9sec2A – 9tan2A
= 9(sec2A – tan2A)
= 9 (1)            [as sec2 A – tan2 A = 1]
= 9
Hence alternative (B) is correct.

(ii) (1 + tanθ + secθ) (1 + cotθ – cosecθ)
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 26
Hence alternative (C) is correct.

(iii) (secA + tanA) (1 – sinA)
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 27

(iv) \(\frac { 1+{ tan }^{ 2 }A }{ 1+{ cot }^{ 2 }A } =\)
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 28

Question 5. Prove the following identities, where the angles involved are acute angles for which the
expressions are defined.
(i) \(\left( cosec\theta -cot\theta \right) ^{ 2 }=\frac { 1-cos\theta }{ 1+cos\theta } \)
(ii) \(\frac { cosA }{ 1+sinA } +\frac { 1+sinA }{ cosA } =2secA\)
(iii) \(\frac { tan\theta }{ 1-cot\theta } +\frac { cot\theta }{ 1-tan\theta } =1+sec\theta cosec\theta \)
(iv) \(\frac { 1-secA }{ secA } =\frac { { sin }^{ 2 }A }{ 1-cosA } \)
(v) \(\frac { cosA-sinA+1 }{ cosA+sinA-1 } =cosecA+cotA\) using the identity cosec2A = 1+cot2A.
(vi) \(\sqrt { \frac { 1+sinA }{ 1-sinA } } =\quad secA+tanA\)
(vii) \(\frac { sin\theta -{ 2sin }^{ 3 }\theta }{ { 2cos }^{ 3 }\theta -cos\theta } =tan\theta \)
(viii) (sin A + cosec A)2 + (cos A + sec A)2 = 7+tan2A+cot2A
(ix) \(\left( cosecA-sinA \right) \left( secA-cosA \right) =\frac { 1 }{ tanA+cotA } \)
(x) \(\left( \frac { 1+{ tan }^{ 2 }A }{ 1+cot^{ 2 }A } \right) ^{ 2 }=\left( \frac { 1-{ tan }A }{ 1-cotA } \right) ^{ 2 }={ tan }^{ 2 }A\)

Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 29

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 30

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 31

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 32

(v) \(\frac { cosA-sinA+1 }{ cosA+sinA-1 } =cosecA+cotA\) using the identity cosec2A = 1+cot2A.
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 33

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 34

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 35

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 36

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 37

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry 38

We hope the NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4, drop a comment below and we will get back to you at the earliest.

Filed Under: CBSE Tagged With: NCERT Solutions for Class 10 Maths

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