Unit Test: Introduction to Trigonometry | Mathematics (Maths) Class 10 PDF Download

Time: 1 hour

M.M. 30

Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.
• Question numbers 6 to 8 carry 2 marks each.
• Question numbers 9 to 11 carry 3 marks each.
• Question number 12 & 13 carry 5 marks each.

Q1: When cos A = 4/5, the value for tan A is (1 Mark)
(a) 3/5
(b) 3/4
(c) 5/3
(d) 4/3

Q2: Here,  sinθ = a/b , so cosθ is equal to (1 Mark)
(a) a/√(b2– a2)
(b) b/a
(c) √(b2-a2)/b
(d) b/√(b2-a2)

Q3: True/ False (1 Mark)
tan 47°/cot 43° = 1

Q4: True/ False (1 Mark)
The value for the expression (cos²23° – sin²67°) will be positive.

Q5: True/ False (1 Mark)
The value for the expression (sin 80° – cos 80°) is negative.

Q6: Prove (√3+1) (3 – cot 30°) = tan3 60° – 2 sin 60° (2 Marks)

Q7: What is the value of (cos²67° – sin²23°)? (2 Marks)

Q8: If 7sin²θ + 3cos²θ = 4, then find the value of tan θ. (2 Marks)

Q9: When sec 4A = cosec (A – 20°), here 4A is an acute angle, find out the value of A. (3 Marks)

Q10: When tan (A + B) = √3 and tan (A – B) = 1/√3 ,0° < A + B ≤ 90°; A > B, find A and B. (3 Marks)

Q11:  If ∠A and ∠B are the acute angles such that cos A = cos B, then show that ∠ A = ∠ B. (3 Marks)

Q12: In triangle ABC, right-angled at B, when tan A = 1/√3 find out the value : (5 marks)
(i) sin A cos C + cos A sin C
(ii) cos A cos C – sin A sin C

Q13: In ∆ ABC, the right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (5 Marks)
(i) sin A, cos A
(ii) sin C, cos C