NCERT Solutions for Class 10 Maths Exercise 8.3 of Chapter 8 Introduction to Trigonometry

NCERT Solutions for Class 10 Maths Exercise 8.3 of Chapter 8 Introduction to Trigonometry are presented here by Future Study Pointed free of cost. These NCERT Solutions of Exercise 8.3-Introduction to Trigonometry will boost your preparation of the forthcoming exams and in doing your homework and class assignments.You can study here all the exercises of the chapter 8-Introduction to Trigonometry.All questions are solved by an expert of maths as per the CBSE norms prescribed for class 10 standard.

The NCERT Solutions for class 10 maths are the most important study material for class 10 in clearing their doubts on maths. The marks in mathematics play an important role in increasing your aggregate percentage in the result of the CBSE board exam, so every student required special attention in mathematics.

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NCERT Solutions for Class 10 Maths  Chapter 8 Introduction to Trigonometry

Exercise 8.1- Introduction to Trigonometry

Exercise 8.2 -Introduction to Trigonometry

Exercise 8.3-Introduction to Trigonometry

Exercise 8.4-Introduction to Trigonometry

NCERT solutions of Important Questions-Introduction to Trigonometry

Latest Sample paper Class 10 maths for Term 1 2021 CBSE board

NCERT Solutions for Class 10 Maths Exercise 8.3 of Chapter 8 Introduction to Trigonometry

Q1.Evaluate

Ans.

(i) sin 18°/cos 72°

Since sin θ = cos (90°-θ)

⇒sin18°=cos(90°-18°)

Substituting the value of sin 18°

cos(90°-18°)/cos 72°

cos 72°/cos 72° = 1

(ii) tan 26°/cot 64°

Since tan θ = cot (90°-θ)

⇒tan26°=cot(90°-26°)

Substituting the value of tan26°

cot(90°-26°)/cot 72°

cot 72°/cot72° = 1

(iii) cos 48° – sin 42°

Since cos θ = sin (90°-θ)

⇒cos 48°=sin(90°-48°)

Substituting the value of sin 18°

sin(90°-48°)° – sin 42°

sin 42° – sin 42° = 0

(iv) cosec 31° – sec 59°

Since cosec θ = sec (90°-θ)

⇒cosec 31°=sec(90°-31°)

Substituting the value of cosec 31°

sec(90°-31°) – sec 59°

sec 59° – sec 59° = 0

Q2.Show that:
(i) tan 48° tan 23° tan 42° tan 67° = 1
(ii) cos 38° cos 52° – sin 38° sin 52° = 0

Ans.

(i) tan 48° tan 23° tan 42° tan 67° = 1

Since tan θ = cot (90°-θ)

⇒tan 48°=cot(90°-48°) and ⇒tan 43°=cot(90°-43°)

Substituting the value of tan 48° and tan 43°

cot(90°-48°) cot(90°-43°) tan 42° tan 67°

cot42° cot67° tan 42° tan 67°

Substituting cot42° =1/tan42° and cot67° =1/tan67°

(1/tan42°) (1/tan 67° )tan 42° tan 67° = 1

(ii) cos 38° cos 52° – sin 38° sin 52° = 0

Since cos θ = sin (90°-θ)

⇒cos 38°=sin(90°-38°) and ⇒sin38°=cos(90°-38°)

Substituting the value of cos38° and sin38°

sin(90°-38°). cos 52°- cos(90°-38°).sin 52°

sin 52°.cos 52° – cos 52°sin 52° = 0

Q3.If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A

Ans. The given equation is

tan 2A = cot (A – 18°), where 2A is an acute angle

cot (90°-2A) = cot (A – 18°)

90°-2A = A – 18°

A + 2A =90°+ 18°=108°

3A = 108°

A = 36°

Q4.If tan A = cot B, prove that A + B = 90°.

Ans. The given equation is

tan A = cot B

cot (90°-  A) =  cot B

90°-  A =  B

A  + B =90°,Hence proved

Q5.If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A

Ans.The given equation is

sec 4A = cosec (A – 20°),where 4A is an acute angle

cosec (90°- 4A) = cosec (A – 20°)

90°- 4A = A – 20°

A+4A = 90° +20°=110°

5A = 110°

A = 22°

Q6.If A, B and C are interior angles of a triangle ABC, then show that:

Ans.According to angle sum property of triangle

A + B + C= 180°

B + C = 180°- A

Dividing by 2

Q7.Express sin 61° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

Ans. The given expression is

sin 61° + cos 75

cos(90° – 61°) + sin(90°-75°)

cos 29° +sin 15°

NCERT Solutions of  Science and Maths for Class 9,10,11 and 12

NCERT Solutions of class 9 maths

Chapter 1- Number System	Chapter 9-Areas of parallelogram and triangles
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3- Coordinate Geometry	Chapter 11-Construction
Chapter 4- Linear equations in two variables	Chapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s Geometry	Chapter 13-Surface Areas and Volumes
Chapter 6-Lines and Angles	Chapter 14-Statistics
Chapter 7-Triangles	Chapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions of class 9 science 

Chapter 1-Matter in our surroundings	Chapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?	Chapter 10- Gravitation
Chapter3- Atoms and Molecules	Chapter 11- Work and Energy
Chapter 4-Structure of the Atom	Chapter 12- Sound
Chapter 5-Fundamental unit of life	Chapter 13-Why do we fall ill ?
Chapter 6- Tissues	Chapter 14- Natural Resources
Chapter 7- Diversity in living organism	Chapter 15-Improvement in food resources
Chapter 8- Motion	Last years question papers & sample papers

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NCERT Solutions of class 10 maths

Chapter 1-Real number	Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3-Linear equations	Chapter 11- Construction
Chapter 4- Quadratic equations	Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression	Chapter 13-Surface areas and Volume
Chapter 6-Triangle	Chapter 14-Statistics
Chapter 7- Co-ordinate geometry	Chapter 15-Probability
Chapter 8-Trigonometry

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Chapter 1- Chemical reactions and equations	Chapter 9- Heredity and Evolution
Chapter 2- Acid, Base and Salt	Chapter 10- Light reflection and refraction
Chapter 3- Metals and Non-Metals	Chapter 11- Human eye and colorful world
Chapter 4- Carbon and its Compounds	Chapter 12- Electricity
Chapter 5-Periodic classification of elements	Chapter 13-Magnetic effect of electric current
Chapter 6- Life Process	Chapter 14-Sources of Energy
Chapter 7-Control and Coordination	Chapter 15-Environment
Chapter 8- How do organisms reproduce?	Chapter 16-Management of Natural Resources

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NCERT solutions of class 11 maths

Chapter 1-Sets	Chapter 9-Sequences and Series
Chapter 2- Relations and functions	Chapter 10- Straight Lines
Chapter 3- Trigonometry	Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction	Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers	Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities	Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations	Chapter 15- Statistics
Chapter 8- Binomial Theorem	Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

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NCERT solutions of class 12 maths

Chapter 1-Relations and Functions	Chapter 9-Differential Equations
Chapter 2-Inverse Trigonometric Functions	Chapter 10-Vector Algebra
Chapter 3-Matrices	Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants	Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability	Chapter 13-Probability
Chapter 6- Application of Derivation	CBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals