CBSE Class 10 Mathematics Introduction to Trigonometry Worksheet Set A

Question. If x = a (cosec θ + cot θ) and y = b(1 - cosθ) / sin θ, then xy =
(a) a² + b² / a² - b²
(b) a² – b²
(c) ab
(d) a/b

Answer: C

Question. If p sin θ + q cos θ = a and p cos θ – q sin θ = b, then p + a / q + b + q - b / p + a =
(a) 1
(b) a² + b²
(c) 0
(d) 2

Answer: C

Question. If x = r sinA cos C, y = r sin A sin C, z = r cos A, then
(a) r² = x² + y² + z²
(b) r² = 2xy
(c) r² = x + y + z
(d) r² = y² + z² + 2xy

Answer: A

Question. If (sec²θ) (1 + sinθ) (1 – sinθ) = k, then find the value of k.
(a) sinθ
(b) secθ
(c) 1
(d) cotθ

Answer: C

Question. If cot θ = (15/8), then evaluate (2 + 2sin θ) (1 - sinθ) / (1 + cosθ) (2 - 2cosθ)
(a) 1
(b) 225/64
(c) 156/7
(d) –1

Answer: B

Question. If tan²θ = 1– a², then the value of sec θ + tan3θ cosec θ is
(a) (2 – a²)
(b) (2 – a²)^1/2
(c) (2 – a²)^2/3
(d) (2 – a²)^3/2

Answer: D

Question. If x = a cos²θ + b sin²θ, then (x – a) (b – x) is equal to
(a) (a – b) sinθ cosθ
(b) (a – b)² sin2θ cos²θ
(c) (a – b)² sinθ cosθ
(d) (a – b) sin2θ cos²θ

Answer: B

Question. sin²θ + cosec²θ is always
(a) greater than 1
(b) less than 1
(c) greater than or equal to 2
(d) equal to 2

Answer: C

Question. If x = p sec q and y = q tan θ , then
(a) x² – y² = p²q²
(b) x²q² – y²p² = pq
(c) x²q² – y²p² = 1/p²q²
(d) x²q² – y²p² = p²q²

Answer: D

Question. (cos⁴A – sin⁴A) is equal to
(a) 1 – 2 cos²A
(b) 2 sin² A – 1
(c) sin²A – cos²A
(d) 2 cos²A – 1

Answer: D

Question. If cos A = 3/5, find the value of 9 cot²A – 1.
(a) 1
(b) 16/65
(c) 65/16
(d) 0

Answer: C

Question. cos 1° . cos 2°. cos 3° ......... cos 179° is equal to
(a) –1
(b) 0
(c) 1
(d) 1/√2

Answer: B

Question. If cosec x – cot x = 1/3, where x ≠ 0, then the value of cos²x – sin²x is
(a) 16/25
(b) 9/25
(c) 8/25
(d) 7/25

Answer: D

Question. If cosec x + sin x = a and sec x + cos x = b, then
(a) (a²b)^2/3 + (ab²)^2/3 =1
(b) (ab²)^2/3 + (a²b²)^2/3 =1
(c) a² + b² = 1
(d) b² – a² = 1

Answer: A

Question. If cosec A + cot A = 11/2, then tan A
(a) 21/22
(b) 15/16
(c) 44/117
(d) 11/117

Answer: C

Question. 2 tan30° / 1 + tan²30° is equal to
(a) sin 30°
(b) cos 60°
(c) 1/2
(d) √3/2

Answer: D

Question. sinθ - 2sin³θ / 2cos³θ - cosθ is equal to
(a) sec θ
(b) tan θ
(c) √sec θ −1
(d) cot θ

Answer: B

Question. If tan²θ = 1 – e², then the value of secθ + tan³θ cosec θ is equal to
(a) (1 – e²)^1/2
(b) (2 – e²)^1/2
(c) (2 – e²)^3/2
(d) (1 – e²)^3/2

Answer: C

Question. If sinq + sin³θ = cos²θ, then the value of cos⁶θ – 4cos⁴θ + 8cos²θ is
(a) 1
(b) 4
(c) 2
(d) 0

Answer: B

Question. If cos θ /1 - sin θ + cos θ / 1 + sin θ = 4, then
(a) cos θ = √/2
(b) sin θ = 1/2
(c) θ = 60°
(d) tan θ = 1/√3

Answer: C

Question. 1−tan² 45°/1+tan 45° =
(a) tan 90°
(b) 1
(c) sin 45°
(d) 0

Answer: D

Question. sin 2A = 2 sin A is true when A =
(a) 0°
(b) 30°
(c) 45°
(d) 60°

Answer: A

Question. 2 tan30°/1− tan²30° =
(a) cos 60°
(b) sin 60°
(c) tan 60°
(d) sin 30°

Answer: C

Question. tan θ - cot θ / sin θ cos θ is equal to
(a) sec2 θ + cosec2 θ
(b) cot2 θ – tan2 θ
(c) cos2 θ – sin2 θ
(d) tan2θ – cot2θ

Answer: D

Question. 2 tan² 30°/1+tan 30=° =
(a) sin 60°
(b) cos 60°
(c) tan 60°
(d) sin 30°

Answer: A

Question. 9 sec² A – 9 tan² A =
(a) 1
(b) 9
(c) 8
(d) 0

Answer: B

Question. (1 + tan θ + sec θ) (1 + cot θ– cosec θ) =
(a) 0
(b) 1
(c) 2
(d) –1

Answer: C

Question. The value of tan30° / cot60° is
(a) 1/√2
(b) 1/√3
(c) √3
(d) 1

Answer: D

Question. The value of (sin 45° + cos 45°) is
(a) 1/√2
(b) √2
(c) √3/2
(d) 1

Answer: B

Question. If sin A + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is
(a) 1
(b) 1/2
(c) 2
(d) 3

Answer: A

Question. (sec A + tan A) (1 – sin A) =
(a) sec A
(b) sin A
(c) cosec A
(d) cos A

Answer: D

Question. 1+tan² A / 1+cot² A = L
(a) sec2 A
(b) –1
(c) cot² A
(d) tan² A

Answer: D

Question. The value of (sin 30° + cos 30°) – (sin 60° + cos 60°) is
(a) –1
(b) 0
(c) 1
(d) 2

Answer: B

Question. If sin (A + B) = √3/2 and sin 2B = 1/2, then
(a) tan B = 1
(b) B = 30°
(c) B = 45°
(d) cos A = 1/2

Answer: C

DIRECTIONS : Study the given Case/Passage and answer the following questions.

Case/Passage

In ΔABC, right angled at B

AB + AC = 9 cm and BC = 3cm.

Question. The value of cot C is
(a) 3/4
(b) 1/4
(c) 5/4
(d) None of these

Answer: A

Question. The value of sec C is
(a) 4/3
(b) 5/3
(c) 1/3
(d) None of these

Answer: B

Question. sin²C + cos²C =
(a) 0
(b) 1
(c) –1
(d) None of these

Answer: B

Assertion & Reason

DIRECTIONS : Each of these questions contains an Assertion followed by reason. Read them carefully and answer the question on the basis of following options. You have to select the one that best describes the two statements.
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion: In a right angled triangle, if tan θ = 3/4, the greatest side of the triangle is 5 units.
Reason: (greatest side)² = (hypotenuse)² = (perpendicular)² + (base)².

Answer: A

Question. Assertion : In a right angled triangle, if cos θ = 1/2 and sin θ = √3/2 , then tan θ = √3
Reason: tan θ = sinθ/cosθ

Answer: A

Fill in the Blanks

DIRECTIONS : Complete the following statements with an appropriate word / term to be filled in the blank space(s).

Question. 2 tan² 45° + 3 cos² 30° – sin² 60° = .............
Answer: 7/2

Question. If tan A = 4/3, then sin A ...............
Answer: 4/5

Question. cos45°/ sec30° +  cosec 30°  = ..............
Answer: 3(√3-1)/4

Question. The value of sin A or cos A never exceeds ......
Answer: 1

Question. sin² A + cos² A = ..............
Answer: 1

Question. In a right trianlge ABC, right angled at B, if tan A = 1, sin A cos A = ..........
Answer: 1/2

Question. In Δ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. The value of tan P is ...........
Answer: 12/5

Question. sin 60° cos 30° + sin 30° cos60° = ................
Answer: 1

Question. In Δ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. sin A = ...........
Answer: 7/25

Question. If 15 cot A = 8, sec A = ..............
Answer: 17/8

DIRECTIONS : Read the following statements and write your answer as true or false.

Question. cot A is the product of cot and A.
Answer: False

Question. sin θ = 4/3, for some angle θ.
Answer: False

Question. If ∠B and ∠Q are acute angles such that sin B = sin Q, then ∠B ≠ ∠Q.
Answer: False

Question. The value of tan A is always less than 1.
Answer: False

Question. sec A = 12/5, for some value of angle A.
Answer: True

Question. sin (A + B) = sin A + sin B.
Answer: False

Question. cot A is not defined for A = 0°.
Answer: True

Question. cos A is the abbreviation used for the cosecant of angle A.
Answer: False