How many practice questions are available for Trigonometry?

SparkEd Math offers 60+ practice questions for Trigonometry across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Trigonometry content free on SparkEd Math?

Yes! All Trigonometry content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Trigonometry differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Trigonometry problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Trigonometry content aligned with the ICSE syllabus?

Yes, all Trigonometry questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 10. The content follows the official curriculum structure and exam pattern.

Trigonometry — Class 10 ICSE (2025-26)

About Trigonometry — Class 10 ICSE

Prove trigonometric identities and solve problems on heights and distances. This topic is part of the ICSE Class 10 mathematics syllabus (chapter: Chapter 7). On this page you can practice 59 questions across three difficulty levels — 20 easy, 19 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 34-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Trigonometry

Introduction to Trigonometric Ratios
Fundamental Trigonometric Identities
Strategies for Proving Trigonometric Identities
Applications: Heights and Distances
Advanced Identities & Exam Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Trigonometry — solved examples for Class 10 ICSE

Example 1easy

In a right-angled triangle ABC, right-angled at B, if we define sin A = BC/AC, which of the following statements is conceptually correct?

A)AC is always the longest side.
B)BC is the side adjacent to angle A.
C)The value of sin A can be greater than 1.
D)Angle C must be obtuse.

Step-by-step solution

In a right-angled triangle, the side opposite the right angle (90°) is called the hypotenuse.
The hypotenuse is always the longest side in a right-angled triangle.
Since AC is the hypotenuse (opposite angle B, which is 90°), it must be the longest side.

Answer: AC is always the longest side.

Example 2medium

If tan A = 4/3, and A is an acute angle, what is the value of sin A + cos A?

A)7/5
B)1/5
C)5/7
D)2/5

Step-by-step solution

Given tan A = Opposite/Adjacent = 4/3. Let the opposite side be 4k and the adjacent side be 3k.
Using Pythagoras theorem, Hypotenuse² = (4k)² + (3k)² = 16k² + 9k² = 25k². So, Hypotenuse = 5k.
Now, sin A = Opposite/Hypotenuse = 4k/5k = 4/5 and cos A = Adjacent/Hypotenuse = 3k/5k = 3/5.
Therefore, sin A + cos A = 4/5 + 3/5 = 7/5.

Answer: 7/5

Example 3hard

If the expression (sec θ + tan θ - 1) / (tan θ - sec θ + 1) is simplified, which of the following expressions is it equivalent to?

A)(1 + sin θ) / cos θ
B)(1 - sin θ) / cos θ
C)(1 + cos θ) / sin θ
D)(1 - cos θ) / sin θ

Step-by-step solution

Consider the numerator: sec θ + tan θ - 1. Substitute 1 = sec²θ - tan²θ. So, sec θ + tan θ - (sec²θ - tan²θ).
Factorize: sec θ + tan θ - (sec θ - tan θ)(sec θ + tan θ) = (sec θ + tan θ) [1 - (sec θ - tan θ)] = (sec θ + tan θ) [1 - sec θ + tan θ].
The expression becomes (sec θ + tan θ) [1 - sec θ + tan θ] / (tan θ - sec θ + 1). The term [1 - sec θ + tan θ] cancels out.
Thus, the simplified expression is sec θ + tan θ, which is equal to 1/cos θ + sin θ/cos θ = (1 + sin θ)/cos θ.

Answer: (1 + sin θ) / cos θ

Practice questions on Trigonometry

Q1.easy
What is the exact value of (sin 45° × cos 45°) + tan 45°?
1. A)1/2
2. B)1
3. C)3/2
4. D)2
Show answer
Answer: 3/2
Hint: Recall the values of trigonometric ratios for 45°: sin 45° = cos 45° = 1/√2 and tan 45° = 1.
Q2.easy
A student claimed that if tan(90° - A) = cot A is true, then sec(90° - A) must be equal to -cosec A. What is the error in the student's reasoning?
1. A)The identity tan(90° - A) = cot A is incorrect.
2. B)The sign of the trigonometric ratio does not change for complementary angles in the first quadrant.
3. C)sec(90° - A) is actually equal to tan A.
4. D)The complementary angle identities only apply to angles less than 45°.
Show answer
Answer: The sign of the trigonometric ratio does not change for complementary angles in the first quadrant.
Hint: Remember that for acute angles (0° to 90°), all trigonometric ratios are positive.
Q3.easy
An observer is 100 meters away from the base of a tower. The angle of elevation to the top of the tower is 30°. Which trigonometric ratio would you use to directly find the height of the tower?
1. A)sin 30°
2. B)cos 30°
3. C)sec 30°
4. D)tan 30°
Show answer
Answer: tan 30°
Hint: Draw a right-angled triangle. Identify the known side (adjacent to the angle) and the unknown side (opposite to the angle). Which ratio relates these two?
Q4.medium
Evaluate: (sin 30° + tan 45° - cosec 60°) / (sec 30° + cos 60° + cot 45°)
1. A)(3√3 - 4) / (6 + 3√3)
2. B)0
3. C)1
4. D)(1 - √3) / (1 + √3)
Show answer
Answer: 0
Hint: Recall the exact values of trigonometric ratios for standard angles (30°, 45°, 60°) and substitute them into the expression.
Q5.medium
Simplify the expression: (1 - sin²A) / (1 - cos²A)
1. A)tan²A
2. B)cot²A
3. C)sec²A
4. D)cosec²A
Show answer
Answer: cot²A
Hint: Remember the fundamental trigonometric identity sin²θ + cos²θ = 1. Use it to rewrite the numerator and the denominator.
Q6.medium
If sin 3A = cos (A - 26°), where 3A is an acute angle, find the value of A.
1. A)29°
2. B)30°
3. C)31°
4. D)32°
Show answer
Answer: 29°
Hint: Use the complementary angle identity: sin θ = cos (90° - θ). Equate the angles after applying the identity.
Q7.hard
Given that A and B are complementary angles (A + B = 90°), what is the value of sin²A + sin²B + tan A tan B?
1. A)0
2. B)1
3. C)2
4. D)3
Show answer
Answer: 2
Hint: Use complementary angle identities to express everything in terms of a single angle, then apply fundamental identities.
Q8.hard
Ravi was asked to prove the identity sin⁴θ + cos⁴θ = 1 - 2sin²θcos²θ. His steps are:
1. L.H.S. = sin⁴θ + cos⁴θ
2. = (sin²θ)² + (cos²θ)²
3. = (sin²θ + cos²θ)² - 2sin²θcos²θ
4. = 1² - 2sin²θcos²θ
5. = 1 - 2sin²θcos²θ = R.H.S.
Which of the following statements is true regarding Ravi's proof?
1. A)Step 1 is incorrect.
2. B)Step 3 uses an incorrect algebraic identity.
3. C)The proof is entirely correct.
4. D)Step 5 is not equivalent to R.H.S.
Show answer
Answer: The proof is entirely correct.
Hint: Carefully recall the algebraic identity for a² + b² and the fundamental trigonometric identity sin²θ + cos²θ = 1.
Q9.hard
A man on the top of a tower 100 m high observes a car moving towards the tower at an angle of depression of 30°. After some time, the angle of depression becomes 60°. What is the distance travelled by the car during this time?
1. A)100√3 m
2. B)200/√3 m
3. C)100(√3 - 1) m
4. D)200√3 m
Show answer
Answer: 200/√3 m
Hint: Draw two right-angled triangles. Use the tangent ratio for both angles of depression to find the initial and final distances of the car from the tower.

These are 9 of the 59 questions available for Trigonometry. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.