Login
1:00:00

Unit Test 5: Trigonometry

Class 10 Mathematics (Standard)

Time: 1 Hour Max. Marks: 30

General Instructions:

  • The question paper consists of 15 questions divided into 4 sections: A, B, C, and D.
  • Section A: 6 MCQs of 1 mark each.
  • Section B: 4 Short Answer questions of 2 marks each.
  • Section C: 4 Short Answer questions of 3 marks each.
  • Section D: 1 Case Study based question of 4 marks.
  • Use of calculators is not permitted.
SECTION A (1 Mark Each)
[1] 1. If sin A = 3/4, then cos A is equal to:
[1] 2. The value of (sin 30° + cos 30°) - (sin 60° + cos 60°) is:
[1] 3. If tan A = cot B, then A + B is equal to:
[1] 4. The value of 9sec² A - 9tan² A is:
[1] 5. A pole 6 m high casts a shadow 2√3 m long on the ground, then the Sun's elevation is:
[1] 6. If cos θ = 2/3, then 2sec² θ + 2tan² θ - 7 is equal to:
SECTION B (2 Marks Each)
[2] 7. Evaluate: 2tan² 45° + cos² 30° - sin² 60°.
Answer Preview
[2] 8. If tan(A + B) = √3 and tan(A - B) = 1/√3; 0° < A + B ≤ 90°; A > B, find A and B.
Answer Preview
[2] 9. Prove that (sec A + tan A)(1 - sin A) = cos A.
Answer Preview
[2] 10. A ladder 15 m long makes an angle of 60° with the wall. Find the height of the point where the ladder touches the wall.
Answer Preview
SECTION C (3 Marks Each)
[3] 11. Prove that: (cos A)/(1 + sin A) + (1 + sin A)/(cos A) = 2sec A.
Answer Preview
[3] 12. Prove that: √((1 + sin A)/(1 - sin A)) = sec A + tan A.
Answer Preview
[3] 13. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Answer Preview
[3] 14. If tan θ + sin θ = m and tan θ - sin θ = n, show that m² - n² = 4√(mn).
Answer Preview
SECTION D (Case Study - 4 Marks)
[4] 15. Case Study: Lighthouse

A lighthouse is a tower with a bright light at the top, located at an important or dangerous place regarding navigation (travel over water). The two main purposes of a lighthouse are to serve as a navigational aid and to warn boats of dangerous areas.

An observer from the top of a 75m high lighthouse from the sea level sees the angles of depression of two ships as 30° and 45°.

(i) If one ship is exactly behind the other on the same side of the lighthouse, draw a simple diagram to represent the situation. (1 Mark)
(ii) Find the distance of the ship from the base of the lighthouse which makes an angle of depression of 45°. (1 Mark)
(iii) Find the distance between the two ships. (2 Marks)
Answer Preview
TOTAL SCORE

0 / 6 (MCQ)

(Subjective answers submitted for review)

Solution Key (MCQs)

Q1. (b) √7/4

cos A = √(1 - sin² A) = √(1 - 9/16) = √(7/16) = √7/4.

Q2. (c) 0

(1/2 + √3/2) - (√3/2 + 1/2) = 0.

Q3. (c) 90°

tan A = cot B ⇒ tan A = tan(90° - B) ⇒ A = 90° - B ⇒ A + B = 90°.

Q4. (b) 9

9(sec² A - tan² A) = 9(1) = 9.

Q5. (a) 60°

tan θ = 6 / 2√3 = 3/√3 = √3 ⇒ θ = 60°.

Q6. (b) 0

sec θ = 3/2, tan² θ = 9/4 - 1 = 5/4. 2(9/4) + 2(5/4) - 7 = 18/4 + 10/4 - 7 = 7 - 7 = 0.