NCERT Solutions for Class 10 Maths Exercise 8.1 of Chapter 8 Introduction to Trigonometry - Future Study Point

NCERT Solutions for Class 10 Maths Exercise 8.1 of Chapter 8 Introduction to Trigonometry

NCERT solutions exercise 8.1

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

NCERT Solutions for Class 10 Maths Exercise 8.1 of Chapter 8 Introduction to Trigonometry are created here for your help in boosting your preparation of the class 10 maths CBSE board exam. All questions of class 10 NCERT maths exercise 8.1 Introduction to Trigonometry are solved by a step-by-step method so every student of class 10 can understand the solutions with the clearance of doubts. Here you can study NCERT solutions of other chapters also. These NCERT Solutions class 10 maths exercise 8.1 will clear all your doubts about basic Trigonometry which is required to solve the questions of higher class maths.

NCERT solutions exercise 8.1

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

NCERT Solutions for Class 10 Maths Exercise 8.1 of Chapter 8 Introduction to Trigonometry

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc

Q1. In ΔABC right angled at B,AB = 24 cm,BC = 7 cm. Determine

(i) sin A, cos A

(ii) sin C, cos C

Ans. The given triangle is ΔABC in which AB = 24 cm, BC = 7 cm and ∠B =90°

Chapter 8 ex.8.1 class 10 maths

Applying Pythagoras theorem

AC = √(AB² + BC²) =√(24² + 7²)=√(576 +49) =√(625) = 25 cm

(i)

(ii)

Q2. In the given figure, find tan P – cot R

Q2 class 10 maths ex 8.1

 

 

 

 

 

 

Ans.In the given ΔPQR, we have PR = 13 cm, PQ =12 cm

Applying Pythagoras theorem

QR = √(PR² – PQ²) = √(13² – 12²) = √(169 -144) = √25 = 5

The value of tan P – cot R

tan P – cot R= 0

Q3.If sin A = 3/4, calculate cos A and tan A

Ans. We are given sin A = 3/4

Since sin A = Perpendicular/Hypotenuse

Let perpendicular = 3x and hypotenuse = 4x

Base = √[(4x)²- (3x)²] = √(16x²-9x²) =x√7

Q4.Given 15 cot A = 8,find sin A and sec A

Ans. We are given that

15 cot A = 8

Let Base is 8x and perpendicular is 15x

Applying pythogorus theorem

Hypotenuse = √(Base² + Perpendicular²) = √[(8x)² + (15x)²]= √(64x² + 225x²)= √(289x²) =17x

Q5. Given sec θ = 13/12, calculate all other trigonometric ratios

Ans. We are given that

Let hypotenuse is 13x and base is 12x

Applying Pythagoras theorem

Perpendicular = √(hypotenuse² – base²) =√(13² – 12²)=√(169-144)=√25 = 5

Q6. If ∠ A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

Ans. We are given that

cos A = cos B where ∠A and ∠B are acute angles, the ΔABC must be as follows

Q6 ex 8.1 class 10 maths

 

 

 

 

 

 

Since

cos A = cos B

AC = BC

∠A = ∠B (angles opposite to equal sides in a triangle)

You can see the video for Q1 to Q6 of exercise 8.1

Q7. If cot θ = 7/8,evaluate

(ii) cot²θ

Ans. (i) We are given cot θ = 7/8

Let the base = 7x and perpendicular = 8x

Applying pythogorus theorem

Hypotenuse = √(Base² + Perpendicular²) = √[(7x)² + (8x)²]= √(49x² + 64x²)= √(113x²) =x√113

The given expression

Putting the value of sin θ and cos θ in the given expression

Applying the identity ( x + y)(x -y) = x ² – y²

(ii) The given expression is

cot²θ

Putting the value of cos θ and sin θ

Q8.If 3 cot A = 4, check whether ( 1-tan²A)/(1 +tan²A) = cos²A – sin²A or not

Ans. We are given

3 cot A = 4

Let base = 4x and perpendicular =3x

Applying pythogorus theorem

Hypotenuse = √(Base² + Perpendicular²) = √[(4x)² + (3x)²]= √(16x² + 9x²)= √(25x²) =5x

The value of tan A = p/b = 3x/4x = 3/4, cos A =b/h =4x/5x = 4/5,sin A =p/h=3x/5x = 3/5

Putting the value of tan x, cosx and of sinx in the following equation

LHS = RHS, The equation shown is OK

See the video for Q7 and Q8

Q9. In ΔABC ,right-angled at B ,if tan A = 1/√3 ,find the value of :

(i) sin A cos C + cos A sin C

(ii) cos A cos C – sin A sin C

Ans. We are given that tan A = 1/√3

 

Let BC =x and AB =√3 x

Applying Pythagoras theorem

AC = √(AB² + BC²) = √[(√3x)² + (x)²]= √(3x² + x²)= √(4x²) =2x

Q9.class 10 maths ex.8.1

 

 

 

 

 

 

(i) sin A cos C + cos A sin C

(ii) cos A cos C – sin A sin C

Q10.In ΔPQR ,right angled at Q,PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P,cos P and tan P.

Ans. The given ΔPQR,in which ∠Q=90°, PR + QR = 25 cm and PQ = 5 cm

PR + QR = 25 cm

QR = 25 – PR

Q10 ex.8.1 class 10 maths

Applying Pythogorus theorem

PR² = QR² + PQ²

PR² = (25 – PR)² + PQ²

PR² = 625 + PR²- 50PR + 5²

50PR =650

PR = 13 cm, QR = 25 -13 = 12 cm

sin P = p/h = QR/PR = 12/13

cos P = b/h = PQ/PR = 5/13

tan P = p/h = QR/PQ = 12/5

See the video for Q9,Q10 and Q11

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

NCERT Solutions of class 9 maths

Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions of class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast years question papers & sample papers

CBSE Class 9-Question paper of science 2020 with solutions

CBSE Class 9-Sample paper of science

CBSE Class 9-Unsolved question paper of science 2019

NCERT Solutions of class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT solutions of class 10 science

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

Solutions of class 10 last years Science question papers

CBSE Class 10 – Question paper of science 2020 with solutions

CBSE class 10 -sample paper of science

NCERT solutions of class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 15- Statistics
Chapter 8- Binomial Theorem Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

NCERT solutions of class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
Chapter 6- Application of DerivationCBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

 

Scroll to Top