Assertion (A): tan 1° · tan 2° · tan 3° · ... · tan 89° = 1. Reason (R): tan 45° = 1.

Both A and R are true but R is not the correct explanation of A.

Both A and R are true and R is the correct explanation of A.

Both A and R are true but R is not the correct explanation of A.

A statue 2 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the pedestal is 45° and the angle of elevation of the top of the statue is 60°. (1) Write an expression for the height of the pedestal in terms of its distance from the point of observation. (2) Write an equation relating the total height (pedestal + statue) using the 60° angle. (3) Calculate the height of the pedestal.

(a) h = x; (b) x + 2 = x√3; (c) Height = (√3+1) m.

Class 10 Maths Chapter 8: Introduction to Trigonometry — Important Questions & Sample Paper

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Yes — this page has 44+ original Class 10 Mathematics Chapter 8 (“Introduction to Trigonometry”) important questions with answers (Multiple Choice (MCQ), Assertion–Reason, Short Answer, Short Answer, Long Answer, Case Study). Practise them free, or generate a full CBSE board-pattern sample paper (80 marks) and export it to PDF or Word — in English & Hindi, for 2026-27.

Chapter 8, Introduction to Trigonometry, lays the foundation for understanding right-triangle relationships. It defines the six trigonometric ratios—sine, cosine, tangent, cosecant, secant, and cotangent—for acute angles using the sides of a right triangle. Students learn to calculate these ratios for specific angles (0°, 30°, 45°, 60°, 90°) and apply them to evaluate expressions like 2 sin 30° + 3 tan 45° – 4 cos 60°. The chapter also introduces fundamental identities such as sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ, which are essential for proving statements like (cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ) = 1. Additionally, the concept of complementary angles enables conversion of ratios, e.g., expressing sin 67° + cos 75° in terms of angles between 0° and 45°. Exam questions frequently test evaluation of trigonometric expressions, proof of identities, solving for unknown angles using given conditions (if cos 9α = sin α, find tan 5α), and simplifying expressions using relationships among ratios. Mastery of these topics equips students with problem-solving skills crucial for board exams.

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Mathematics — Introduction to Trigonometry

Class 10Time: 3 hrsMax Marks: 80

SECTION A

1.
Which of the following is equal to tan 60°?
(a) √3(b) 1/√3(c) 1(d) 0
1
2.
If sin(θ – 10°) = 1/2, then the smallest positive angle θ is:
(a) 10°(b) 20°(c) 30°(d) 40°
1
3.
If cos θ = x/y (where x, y > 0 and x < y), then tan θ is:
(a) √(y² – x²)/x(b) x/√(y² – x²)(c) y/√(y² – x²)(d) √(y² – x²)/y
1

+ 41 more questions in the full paper

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Marks distribution & blueprint

In a CBSE exam, this chapter typically contributes questions across the following types. The last column shows how many original questions of each type we have ready in our bank for this chapter:

Question type	Marks each	In our bank
Multiple Choice (MCQ)	1 mark	13
Assertion–Reason	1 mark	6
Short Answer	2 marks	8
Short Answer	3 marks	6
Long Answer	5 marks	5
Case Study	4 marks	6

44 original, exam-style questions in our bank for this chapter — with answers.

Important & sample questions (with answers)

Real, exam-style questions to practise and revise — each with its answer. Generate a full paper for unlimited more.

Q1. Which of the following is equal to tan 60°?
1 mark
Multiple Choice (MCQ)
(A) √3(B) 1/√3(C) 1(D) 0
▸ Answer▾ Answer
√3
Q2. If sin(θ – 10°) = 1/2, then the smallest positive angle θ is:
1 mark
Multiple Choice (MCQ)
(A) 10°(B) 20°(C) 30°(D) 40°
▸ Answer▾ Answer
40°
Q3. If cos θ = x/y (where x, y > 0 and x < y), then tan θ is:
1 mark
Multiple Choice (MCQ)
(A) √(y² – x²)/x(B) x/√(y² – x²)(C) y/√(y² – x²)(D) √(y² – x²)/y
▸ Answer▾ Answer
√(y² – x²)/x
Q4. If sec θ + tan θ = p, then the value of sec θ – tan θ is:
1 mark
Multiple Choice (MCQ)
(A) p(B) 1/p(C) p²(D) 1/p²
▸ Answer▾ Answer
1/p
Q5. Assertion (A): tan 1° · tan 2° · tan 3° · ... · tan 89° = 1. Reason (R): tan 45° = 1.
1 mark
Assertion–Reason
(A) Both A and R are true and R is the correct explanation of A.(B) Both A and R are true but R is not the correct explanation of A.(C) A is true but R is false.(D) A is false but R is true.
▸ Answer▾ Answer
Both A and R are true but R is not the correct explanation of A.
Q6. If x = a sin θ and y = b tan θ, prove that a²/x² - b²/y² = 1.
2 marks
Short Answer
▸ Answer▾ Answer
a²/x² - b²/y² = 1
Q7. If sin(A + B) = √3/2 and cos(A - B) = 1/2, where 0° < A + B ≤ 90° and A > B, find the angles A and B.
2 marks
Short Answer
▸ Answer▾ Answer
A = 60°, B = 0°
Q8. If sin A + sin² A = 1, find the value of cos² A + cos⁴ A.
3 marks
Short Answer
▸ Answer▾ Answer
1
Q9. Evaluate: 2 sin 30° + 3 tan 45° – 4 cos 60°.
3 marks
Short Answer
▸ Answer▾ Answer
2
Q10. If sin A + cos A = √2, find the value of tan A + cot A.
5 marks
Long Answer
▸ Answer▾ Answer
2
Q11. If 5 sin θ = 4 and θ is an acute angle, find the value of (3 tan θ - 4 cos θ) / (3 sec θ + 4 cosec θ).
5 marks
Long Answer
▸ Answer▾ Answer
4/25
Q12. A statue 2 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the pedestal is 45° and the angle of elevation of the top of the statue is 60°.
4 marks
Case Study
1. (i) Write an expression for the height of the pedestal in terms of its distance from the point of observation.1 mark
2. (ii) Write an equation relating the total height (pedestal + statue) using the 60° angle.1 mark
3. (iii) Calculate the height of the pedestal.2 marks
▸ Answer▾ Answer
(a) h = x; (b) x + 2 = x√3; (c) Height = (√3+1) m.

Frequently asked questions

What are the key trigonometric ratios I must memorize for the Class 10 board exam?

You should memorize the values of sin, cos, tan, cosec, sec, and cot for 0°, 30°, 45°, 60°, and 90°. These standard angles form the basis for evaluating expressions and are often not provided in the exam.

Which trigonometric identities are most important from this chapter?

The three fundamental identities are: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ. They are crucial for proving complex expressions and simplifying equations.

What types of questions are typically asked from Introduction to Trigonometry?

Common question types include: evaluating expressions involving standard angles (e.g., 2 sin 30° + 3 tan 45° – 4 cos 60°), proving trigonometric identities, using complementary angle relationships, and solving for an angle given a relation like sin θ = cos θ.

How can I prepare for proving trigonometric identity questions?

Start by simplifying one side of the identity to match the other. Convert all ratios to sin and cos if stuck, use algebraic manipulation, and apply the standard identities. Regular practice with varied problems, like (cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ) = 1, builds confidence.

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Important & sample questions (with answers)

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