Question 1

If cos(42°) = 0.743, then sin(48°) = ?

Accepted Answer

Step 1: Recognize that 42° and 48° are complementary angles (42° + 48° = 90°). Step 2: Apply the complementary angle property: cos(θ) = sin(90° − θ). Step 3: Therefore, cos(42°) = sin(90° − 42°) = sin(48°). Step 4: Since cos(42°) = 0.743, we have sin(48°) = 0.743.

Question 2

cot(67°) = tan(x°). Find the value of x.

Accepted Answer

Step 1: Recall that cot(θ) = tan(90° − θ). Step 2: Apply this property: cot(67°) = tan(90° − 67°) = tan(23°). Step 3: Therefore, tan(x°) = tan(23°), which means x = 23.

Question 3

If sin(35°) = k, then what is the value of cos(55°)?

Accepted Answer

Step 1: Recognize that 35° and 55° are complementary angles (35° + 55° = 90°). Step 2: Apply the complementary angle property: sin(θ) = cos(90° − θ). Step 3: Therefore, sin(35°) = cos(55°). Step 4: Since sin(35°) = k, we have cos(55°) = k.

Question 4

sin(15°) × cosec(75°) + cos(15°) × sec(75°) = ?

Accepted Answer

Step 1: Recognize that 15° and 75° are complementary angles (15° + 75° = 90°). Step 2: Apply complementary angle properties: cosec(75°) = sec(15°) and sec(75°) = cosec(15°). Step 3: Substitute: sin(15°) × sec(15°) + cos(15°) × cosec(15°). Step 4: Simplify: sin(15°)/cos(15°) + cos(15°)/sin(15°) = tan(15°) + cot(15°). Step 5: Alternatively, use: sin(15°) × sec(15°) = sin(15°)/cos(15°) = tan(15°) and cos(15°) × cosec(15°) = cos(15°)/sin(15°) = cot(15°). Step 6: tan(15°) + cot(15°) = sin²(15°) + cos²(15°) / [sin(15°)cos(15°)] = 1 / [sin(15°)cos(15°)] = 2/sin(30°) = 2/(1/2) = 4.

Question 5

If sec(36°) = m, then what is cosec(54°)?

Accepted Answer

Step 1: Recognize that 36° and 54° are complementary angles (36° + 54° = 90°). Step 2: Apply the complementary angle property: sec(θ) = cosec(90° − θ). Step 3: Therefore, sec(36°) = cosec(90° − 36°) = cosec(54°). Step 4: Since sec(36°) = m, we have cosec(54°) = m.

Question 6

tan(28°) × tan(62°) = ?

Accepted Answer

Step 1: Observe that 28° + 62° = 90°, so these are complementary angles. Step 2: Apply the complementary angle property: tan(θ) × tan(90° − θ) = 1. Step 3: Therefore, tan(28°) × tan(62°) = tan(28°) × cot(28°) = 1.

Question 7

If tan(62°) × tan(28°) = x, what is the value of x?

Accepted Answer

Step 1: Observe that 62° + 28° = 90°, so these angles are complementary. Step 2: For complementary angles, tan(θ) × tan(90° - θ) = tan(θ) × cot(θ). Step 3: Since cot(θ) = 1/tan(θ), we have tan(θ) × cot(θ) = 1. Step 4: Therefore, tan(62°) × tan(28°) = 1.

Question 8

A ladder leans against a wall such that it makes an angle of 58° with the ground. What angle does the ladder make with the wall?

Accepted Answer

Step 1: The ladder, wall, and ground form a right triangle where the right angle is at the base of the wall. Step 2: The angle between the ladder and the ground is 58°. Step 3: The angle between the ladder and the wall is complementary to the angle with the ground. Step 4: Therefore, the angle with the wall = 90° - 58° = 32°.

Question 9

If cos(18°) = p, what is sin²(72°) + cos²(18°) equal to?

Accepted Answer

Step 1: Recognize that 18° + 72° = 90°, so these angles are complementary. Step 2: Apply the complementary angle identity: sin(72°) = sin(90° - 18°) = cos(18°) = p. Step 3: Rewrite the expression: sin²(72°) + cos²(18°) = p² + p². Step 4: Simplify: p² + p² = 2p².

Question 10

If cot(47°) = m, express tan(43°) in terms of m.

Accepted Answer

Step 1: Observe that 47° + 43° = 90°, so these angles are complementary. Step 2: Apply the complementary angle identity: tan(θ) = cot(90° - θ). Step 3: Therefore, tan(43°) = cot(90° - 43°) = cot(47°). Step 4: Since cot(47°) = m, we have tan(43°) = m.

Question 11

If sin(35°) = k, then what is the value of cos(55°) in terms of k?

Accepted Answer

Step 1: Recognize that 35° and 55° are complementary angles (35° + 55° = 90°). Step 2: Apply the complementary angle identity: sin(θ) = cos(90° - θ). Step 3: Therefore, sin(35°) = cos(90° - 35°) = cos(55°). Step 4: Since sin(35°) = k, we have cos(55°) = k.

Question 12

Given tan(4β − 8°) · cot(2β + 14°) = 1 and both angles are acute, find the value of [sin(β + 11°) − cos(β + 11°)]² + 2sin(β + 11°)cos(β + 11°).

Accepted Answer

Step 1: tan(A) · cot(B) = 1 implies A = B, so 4β − 8° = 2β + 14°. Step 2: 2β = 22°, giving β = 11°. Step 3: We need [sin(11° + 11°) − cos(11° + 11°)]² + 2sin(11° + 11°)cos(11° + 11°) = [sin(22°) − cos(22°)]² + 2sin(22°)cos(22°). Step 4: Expanding: sin²(22°) − 2sin(22°)cos(22°) + cos²(22°) + 2sin(22°)cos(22°). Step 5: The middle terms cancel: sin²(22°) + cos²(22°) = 1.

Question 13

Given that sin(α) = cos(2β) and cos(α) = sin(2β), where α and 2β are both acute angles, find sin(α + 2β).

Accepted Answer

Step 1: From sin(α) = cos(2β), we get sin(α) = sin(90° − 2β), so α = 90° − 2β (since both are acute). Step 2: From cos(α) = sin(2β), we get cos(α) = cos(90° − 2β), which also gives α = 90° − 2β. Step 3: Both conditions are consistent. Step 4: α + 2β = (90° − 2β) + 2β = 90°. Step 5: sin(90°) = 1.

Question 14

If tan(3x − 15°) · cot(2x + 25°) = 1 and both angles are acute, find the value of sin²(x + 5°) + cos²(x + 5°) − 2sin(x + 5°)cos(x + 5°).

Accepted Answer

Step 1: tan(A) · cot(B) = 1 implies tan(A) = tan(B), so 3x − 15° = 2x + 25° (for acute angles). Step 2: x = 40°. Step 3: We need sin²(x + 5°) + cos²(x + 5°) − 2sin(x + 5°)cos(x + 5°). Step 4: sin²(45°) + cos²(45°) − 2sin(45°)cos(45°). Step 5: Using the identity sin²(θ) + cos²(θ) = 1 and 2sin(θ)cos(θ) = sin(2θ): 1 − sin(90°) = 1 − 1 = 0.

Question 15

If sec(2α + 10°) = cosec(3α − 20°) where both angles are acute, find the value of sin(α + 15°) + cos(α + 15°).

Accepted Answer

Step 1: sec(A) = cosec(B) implies cos(A) = sin(B), which means A + B = 90° (complementary angles). Step 2: (2α + 10°) + (3α − 20°) = 90°. Step 3: 5α − 10° = 90°, so 5α = 100°, giving α = 20°. Step 4: We need sin(20° + 15°) + cos(20° + 15°) = sin(35°) + cos(35°). Step 5: sin(35°) + cos(35°) = √2 · sin(35° + 45°) = √2 · sin(80°) = √2 · cos(10°). Step 6: Using exact values or the identity sin(θ) + cos(θ) = √2 · sin(θ + 45°), we get √2 · sin(80°). Numerically, sin(35°) ≈ 0.574 and cos(35°) ≈ 0.819, so the sum ≈ 1.393 ≈ √2 · sin(80°) ≈ √2 · 0.985 ≈ 1.393. The exact answer is √2 · sin(80°) or equivalently √(2 + 2sin(70°)).

IBPS RRB PO Complementary Angles

IBPS RRB PO Complementary Angles — Past Exam Questions

Complementary Angles— Rules & Concept

Key Points to Remember

Exam-Specific Tips

60-Second Revision — Complementary Angles