Trigonometric Identities Quiz - CBSE Class 10 Mathematics

Free practice quiz: Trigonometric Identities (CBSE Class 10 Mathematics). 15 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 10 Mathematics practice quiz has 15 multiple-choice questions on Trigonometric Identities, and 15 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

About this topic

Trigonometric ratios link an acute angle of a right triangle to its side lengths. Identities connect the ratios to each other. Heights and Distances applies these ratios to real situations using angles of elevation and depression.

• In a right triangle, ratios depend only on the angle, not on the triangle's size.
• Six ratios: sin, cos, tan and their reciprocals cosec, sec, cot.
• Standard angles: 0°, 30°, 45°, 60°, 90° have fixed ratio values.
• Knowing one ratio, you can find all others using a triangle or identities.
• Angle of elevation: looking up from the horizontal line to the object.
• Angle of depression: looking down from the horizontal line to the object.
• Heights and Distances: draw a right triangle, mark the angle, pick the right ratio.

Sample questions

1. For an acute angle A, which of the following is always true?

   1. sin²A + cos²A = 1
   2. sin²A − cos²A = 1
   3. sin²A + cos²A = 0
   4. sin²A × cos²A = 1
   Show answer

   Answer: A. sin²A + cos²A = 1

   The fundamental Pythagorean identity states sin²A + cos²A = 1 for every angle A.

2. If sin A = 3/5 and A is acute, then cos A equals:

   1. 4/5
   2. 3/5
   3. 2/5
   4. 5/3
   Show answer

   Answer: A. 4/5

   cos²A = 1 − sin²A = 1 − 9/25 = 16/25. Since A is acute, cos A = 4/5.

3. For an acute angle A, sec²A − 1 equals:

   1. tan²A
   2. cot²A
   3. 1
   4. 0
   Show answer

   Answer: A. tan²A

   Rearrange sec²A − tan²A = 1 to get sec²A − 1 = tan²A.

4. (1 + tan² A) cos² A equals:

   1. 1
   2. sec²A
   3. tan²A
   4. cos²A
   Show answer

   Answer: A. 1

   1 + tan²A = sec²A, so sec²A × cos²A = 1.

5. (cosec A + cot A)(cosec A − cot A) equals:

   1. 0
   2. 1
   3. cosec²A + cot²A
   4. 2 cosec A cot A
   Show answer

   Answer: B. 1

   Difference of squares gives cosec²A − cot²A = 1.

More questions in this quiz

Answers and explanations are in the full quiz.

1. For an acute angle A, which statement is an identity?
2. For an acute angle A, 1 + cot²A equals:
3. (1 + cot² A) sin² A equals:
4. For an acute angle A, 1 − sin²A is equal to:
5. cosec² 60° − cot² 60° equals:
6. If tan A = 5/12 and A is acute, then sec A equals:
7. sin² 30° + cos² 30° equals:
8. (sec A + tan A)(sec A − tan A) equals:
9. If cosec A = 13/5 and A is acute, then cot A equals:
10. (1 − sin² A) ÷ cos A equals:

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