Class 10 Maths Trigonometry MCQ’s With Solutions for Term-1 CBSE Board Exam 2021

Class 10 Maths Trigonometry MCQ’s With Solutions for Term-1 CBSE Board Exam 2021 are created for boosting your preparation of Maths subject in Term-1 CBSE Board exam 2021 which is going to be held in the month of November-December.We have planned to introduce bunches of Maths MCQ’s with their detail solutions for achieving excellent marks for our readers so the students who didn’t subscribe our website and Utube channel,those are requested to do that as soon as possible.These Maths MCQ’s are created and collected as per the Maths sample paper published by CBSE,hence these Maths MCQ questions of Trigonometry are very important inputs for the Term-1 CBSE exams and are based on the chapter 8-introduction to Trigonometry.

Class 10 Maths Trigonometry MCQ’s With Solutions for Term-1 CBSE Board Exam 2021

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Q1. Given that sin α = 1/2 and cos β = 1/2,then the value of α + β is

(a) 0° (b) 30° (c) 60° (d) 90°

Ans.(d) 90°

sin α = 1/2 ⇒sin α = sin 30° ⇒α = 30°

cos β = 1/2 ⇒cos β = cos 60° ⇒β = 60°

α + β = 30° +60° = 90°

Q2.If 4tan θ = 3, then (4 sin θ – cos θ)/(4 sin θ +cos θ) is equal to

(a) 2/3 (b) 1/3 (c) 1/2 (d) 3/4

Ans.(c) 1/2

We are given that 4tan θ = 3

tan θ = 3/4 = perp./Base

Hypotenuse = √(3² +4²) =√25 =5

sin θ = 3/5 and cos θ = 4/5

(4 sin θ – cos θ)/(4 sin θ +cos θ)

( 4×3/5 – 4/5)(4×3/5 + 4/5)

(12/5 – 4/5)(12/5 + 4/5)

$=\frac{(12-4)/5}{(12+4)/5)}$

= 8/16 = 1/2

Q3.sin (45° + θ) – cos (45° -θ) is equal to

(a) 2 cos θ (b) 0 (c) 2 sin θ (d) 1

sin (45° + θ) – sin [90° -(45° -θ)]

sin (45° + θ) -sin (90° -45° + θ)

sin (45° + θ) -sin (45° + θ) =0

Q4.If √2 sin (60° – α) = 1 ,then α is

(a) 45° (b) 15° (c) 60° (d) 30 °

Ans. (b) 15°

√2 sin (60° – α) = 1

sin (60° – α) = 1/√2

sin (60° – α) = sin 45°

60° – α = 45°

α = 60° – 45° = 15°

Q5. The value of sin²30° – cos² 30° is

(a) -1/2 (b) √3/2 (c) 3/2 (d) -2/3

Ans. (a) -1/2

The given expression is

sin²30° – cos² 30°

Value of sin 30° = 1/2 and of cos 30°= √3/2

(1/2)² -(√3/2)²

1/4 – 3/4 = -2/4 = -1/2

Q6.If √2 sin (60° – α) =1,then α is

(a) 45° (b) 15° (c) 60° (d) 30°

Ans.(b) 15°

We are given

√2 sin (60° – α) =1

sin (60° – α) = 1/√2 = sin 45°

60° – α = 45°

α = 60° – 45° = 15°

Q7. The maximum value of 1/ cosec α is

(a) 0 (b) 1 (c) √3/2 (d) -1/√2

Ans. (b) 1

The given expression is

1/ cosec α

= sin α

The maximum value of sin α is 1

Class 10 Maths Trigonometry MCQ’s With Solutions for Term-1 CBSE Board Exam 2021

Q8.If cos (40°+A) = sin 30°,then value of A is

(a) 30° (a) 40° (a) 60° (a) 20°

Ans. (a) 20°

The given trigonometric equation is

cos (40°+A) = sin 30°

Applying the formula sin θ = cos (90° -θ)

cos (40°+A) = cos (90°- 30°)

40°+A = 90°- 30°=60°

A = 60° – 40° = 20°

See the Videoes-NCERT Solutions of Exercise 8.4 Introduction to Trigonometry

Q9.If cosec θ – cot θ = 1/3 , the value of (cosec θ + cot θ) is

(a) 1 (b) 2 (c) 3 (d) 4

Ans.(c) 3

The given trigonometric equation is

cosec θ – cot θ = 1/3

cosec θ – cot θ = (cosec²θ -cot²θ)/3

cosec θ – cot θ = (cosec θ – cot θ)(cosec θ + cot θ)/3

(cosec θ + cot θ) = 3

Q10. (1 + tan²A)/(1 + cot²A) is equal to

(a) sec²A (b) -1 (c) cot²A (d) tan²A

Ans. (d) tan²A

(1 + tan²A)/(1 + cot²A)

$=\frac{1+sin^{2}A/cos^{2}A}{1+cos^{2}A/sin^{2}A}$

$=\frac{\left ( cos^{2}A+sin^{2}A \right )/cos^{2}A}{\left ( cos^{2}A+sin^{2}A \right )/sin^{2}A}$

$=\frac{sin^{2}A}{cos^{2}A}=tan^{2}A$

Q11.If cos A + cos²A =1,then sin²A +Sin⁴A is equal to

(a) -1 (b) 0 (c) 1 (d) None of these

Ans. (c) 1

The given trigonometric equation is

cos A + cos²A =1

cos A = 1 – cos²A = sin²A

sin²A +sin⁴A

cos A + (sin²A)²

cos A + (cos A)²

cos A + cos²A =1

Q12.2(sin⁶A + cos⁶A) -3(sin⁴A + cos⁴A) is equal to

(a) 0 (b) 6 (c) -1 (d) None of these

Ans. (c) -1

2(sin⁶A + cos⁶A) -3(sin⁴A + cos⁴A)

2[ (sin²A)³ + (cos²A)³] -3[(sin²A)² + (cos²A)²]

2(sin²A + cos²A)[(sin²A)² + (cos²A)²- sin²A.cos²A] – 3[(sin²+cos²A)²-2sin²A.cos²A ]

2[( sin ²A + cos²A)² -2sin²A.cos²A -sin²A.cos²A] – 3( 1 – 2sin²A. 2cos²A )

2( 1- 3sin²A.cos²A) -3( 1 – 2sin²A. 2cos²A )

2 -6 sin²A.cos²A – 3 +6sin²A. 2cos²A = -1

Class 10 Maths Trigonometry MCQ’s With Solutions for Term-1 CBSE Board Exam 2021

Q13.3 sin² 20° – 2 tan² 45° + 3 sin² 70° is equal to

(a) 0 (b) 1 (c) 2 (d) -1

Ans.(b) 1

The given expression is

3 sin² 20° – 2 tan² 45° + 3 sin² 70°

3 sin²(90° – 70°) + 3 sin² 70°-2 tan² 45°

3 cos² 70° + 3 sin² 70°- 2

3(cos² 70° + sin² 70°) -2

3 -2 = 1

Q14. If sin 2A = 1/2(tan²45°) where A is an acute angle, then the value of A is

(a) 60° (b) 45° (c) 30° (d) 15°

Ans. (d) 15°

The given equation is

sin 2A = 1/2(tan²45°)

sin 2A = 1/2 = sin 30°

2A = 30°

A = 15°

Q15. sin θ/(1 + cos θ) is

(a) cos θ/(1 – sin θ) (b) (1-sin θ)/sin θ (c) (1-sin θ)/cos θ (d) (1-cos θ)/sin θ

Ans. (d) (1-cos θ)/sin θ

The given expression is

sin θ/(1 + cos θ)

Multiplying the numerator and denominator by the conugate of the denominator (1 – cos θ)

sin θ(1-cos θ)/(1 + cos θ)(1-cos θ)

=sin θ(1-cos θ)/(1-cos² θ)

= sin θ(1-cos θ)/sin² θ

=(1-cos θ)/sin θ

Q16.If A + B = 90°, cot B = 3/4 ,then tan A is equal to

(a) 5/3 (b) 1/3 (c) 3/4 (d) 1/4

Ans. (c) 3/4

We are given that

A + B = 90°

A = 90° – B

tan A = tan (90° – B)

tan A = cot B

Also given to us ,cot B = 3/4

tan A = 3/4

Class 10 Maths Trigonometry MCQ’s With Solutions for Term-1 CBSE Board Exam 2021

Q17. If A and B are complementary angles then

(a) sin A = sin B (b) cos A = cos B (c) tan A = tan B (d) sec A = cosec B

Ans. (d) sec A = cosec B

We are given that A and B are complementary angles

Therefore

A + B = 90°

sec A = sec( 90° – B) = cosec B

Q18. The value of tan 1° tan 2° tan 3°……tan 87° tan 88° tan 89°

(a) 1 (b) -1 (c) 0 (d) None of these

Ans.(a) 1

The given expression is

tan 1° tan 2° tan 3°……tan 87° tan 88° tan 89°

=tan(90°-89°) tan (90°-88°) tan (90°-87°)…..tan 87° tan 88° tan 89°

= cot 89°. cot 88°.cot 87°…..tan 87° tan 88° tan 89°

= (1/tan 87°).1/ tan 88°.1/ tan 89°….tan 87° tan 88° tan 89°

= 1

Q19.The value of cos 1° cos 2° cos 3°…… cos 180°

(a) 1 (b) -1 (c) 0 (d) None of these

Ans.(c) 0

We are given that

cos 1° cos 2° cos 3°…… cos 180°

=cos 1° cos 2° cos 3°..cos 90°cos 91°…. cos 180°

=cos 1° ×cos 2° ×cos 3°..0×cos 91°…. cos 180° = 0

Class 10 Maths Trigonometry MCQ’s With Solutions for Term-1 CBSE Board Exam 2021

Q20. If sec θ + tan θ = x, then sec θ =

(a) (x²+1)/x (b) (x²+1)/2x (c) (x²-1)/2x (d) (x²-1)/x

Ans. (b) (x²+1)/2x

The given equation is

sec θ + tan θ = x….(i)

We have

1 + tan ²θ = sec²θ

sec²θ – tan ²θ = 1

(sec θ – tan θ)(sec θ + tan θ) = 1

Putting the value of x

x (sec θ – tan θ) = 1

sec θ – tan θ = 1/x…..(ii)

Adding both equations (i) and (ii)

2 sec θ = x + 1/x

2 sec θ = (x² +1)/x

sec θ = (x² +1)/2x

Why are these MCQ’S are important to study for the preparation of term-1 Exam 2021 CBSE Board ?

CBSE has changed pattern of the question paper,so according to latest pattern in the maths question paper there will be 50 questions of MCQ each of 1 marks,so this pattern is easier than the previous years question papers,but it is very important to clear the concept of the chapters because maximum questions would be out of the books,hence it is mandatory to study additional questions which are technical and short.

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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

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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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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

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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

Class 10 Maths Trigonometry MCQ’s With Solutions for Term-1 CBSE Board Exam 2021

Class 10 Maths Trigonometry MCQ’s With Solutions for Term-1 CBSE Board Exam 2021

See the Videoes-NCERT Solutions of Exercise 8.4 Introduction to Trigonometry