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IBPS RRB PO Complementary Angles

Study Material — 15 PYQs (2023–2023) · Concept Notes · Shortcuts

IBPS RRB PO Complementary Angles is a frequently tested subtopic — 15 previous year questions from 2023–2023 papers are included below with concept notes, key rules and shortcut tricks.

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2023–2023
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Previous Year Questions

IBPS RRB PO Complementary Angles — Past Exam Questions

15 questions from actual IBPS RRB PO papers · all shown free · click option to reveal solution

Exam Q 12023Previous Year Pattern

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

Exam Q 22023Previous Year Pattern

tan(28°) × tan(62°) = ?

Exam Q 32023Previous Year Pattern

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

Exam Q 42023Previous Year Pattern

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

Exam Q 52023Previous Year Pattern

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

Exam Q 62023Previous Year Pattern

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

Exam Q 72023Previous Year Pattern

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

Exam Q 82023Previous Year Pattern

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

Exam Q 92023Previous Year Pattern

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

Exam Q 102023Previous Year Pattern

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

Exam Q 112023Previous Year Pattern

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?

Exam Q 122023Previous Year Pattern

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

Exam Q 132023Previous Year Pattern

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°).

Exam Q 142023Previous Year Pattern

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

Exam Q 152023Previous Year Pattern

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°).

Concept Notes

Complementary Angles— Rules & Concept

Core ConceptRead this first — the foundation of the topic
SSC CGL typically asks three types of questions

direct formula application, simplification problems, and value finding. Direct questions give you an angle and ask for complementary ratio values. Simplification problems mix multiple complementary ratios in expressions. Value finding questions provide ratio values and ask for complementary angle ratios.

Here's a powerful shortcut: whenever you see (90° - θ) in any trigonometric expression, immediately swap the ratio with its complementary partner. Sin becomes cos, tan becomes cot, sec becomes cosec. This works both ways. If you see sin 60°, think cos 30°.

If you see tan 25°, think cot 65°

Let's solve a typical example
1

Identify complementary angles. Since 30° + 60° = 90°, these are complementary.

2

Apply complementary relationships. cos 60° = cos(90° - 30°) = sin 30°, sin 60° = sin(90° - 30°) = cos 30°.

3

Substitute values. sin 30° × sin 30° + cos 30° × cos 30° = (sin 30°)² + (cos 30°)².

4

Use standard values. sin 30° = 1/2, cos 30° = √3/2.

5

Calculate final answer. (1/2)² + (√3/2)² = 1/4 + 3/4 = 1. Another shortcut involves recognizing patterns. Expression like sin²θ + cos²θ always equals 1. When you see complementary angles multiplied or added in specific patterns, look for these standard identities.

Exam TrapsCommon mistakes students make — avoid these

include forgetting that complementary means sum equals 90°, not 180°. Students often confuse complementary with supplementary angles. Another error is applying relationships incorrectly - remember sin(90° - θ) = cos θ, not sin θ = cos(90° - θ).

Practice identifying complementary pairs quickly: 30°-60°, 45°-45°, 25°-65°, 37°-53°. Most SSC questions use these standard combinations.

Key Points to Remember

  • Complementary angles sum to exactly 90 degrees
  • sin(90° - θ) = cos θ and cos(90° - θ) = sin θ
  • tan(90° - θ) = cot θ and cot(90° - θ) = tan θ
  • sec(90° - θ) = cosec θ and cosec(90° - θ) = sec θ
  • Common complementary pairs: 30°-60°, 45°-45°, 37°-53°
  • Quick trick: swap ratios when you see (90° - θ)
  • sin²θ + cos²θ = 1 for any complementary relationship
  • Complementary means 90°, supplementary means 180°

Exam-Specific Tips

  • sin 30° = 1/2 and cos 60° = 1/2
  • tan 45° = cot 45° = 1
  • sin 37° = cos 53° = 3/5
  • cos 37° = sin 53° = 4/5
  • sin²θ + cos²θ = 1 for all values of θ
  • sec θ × cos θ = 1 for complementary calculations
  • Standard complementary pairs sum to 90°: 30°-60°, 45°-45°, 37°-53°
  • cosec(90° - θ) = sec θ identity appears in 15% of trigonometry questions

60-Second Revision — Complementary Angles

  • Remember: Complementary angles add to 90°, not 180°
  • Formula: sin(90° - θ) = cos θ, cos(90° - θ) = sin θ
  • Shortcut: When you see (90° - θ), swap the trigonometric ratio
  • Key pairs: 30°-60°, 45°-45°, 37°-53° appear most frequently
  • Identity: sin²θ + cos²θ = 1 works for all complementary problems
  • Trap: Don't confuse complementary (90°) with supplementary (180°)
  • Quick check: Verify angle sum equals 90° before applying formulas
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