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SSC CHSL Complementary Angles

Study Material — 2 PYQs (2018–2018) · Concept Notes · Shortcuts

SSC CHSL Complementary Angles is a frequently tested subtopic — 2 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.

2 PYQs
2018–2018
17 Practice
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8 Key Points
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Previous Year Questions

SSC CHSL Complementary Angles — Past Exam Questions

2 questions from actual SSC CHSL papers · all shown free · click option to reveal solution

Exam Q 12018Previous Year Pattern

If tan(θ) = cot(30°), and 0° < θ < 90°, find the value of θ.

Exam Q 22018Previous Year Pattern

If sin(3θ + 15°) = cos(2θ + 25°), where both angles are acute, find the value of θ.

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
Practice MCQs

Complementary Angles — Practice Questions

17graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

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

Practice 2easy

tan(28°) × tan(62°) = ?

Practice 3easy

If cos(42°) = m, then sin(48°) is equal to:

Practice 4easy

If sin(35°) = k, then cos(55°) = ?

Practice 5easy

If cot(42°) = m, then tan(48°) = ?

Practice 6easy

sec(37°) − cosec(53°) = ?

Practice 7medium

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

Practice 8medium

Given that sin(3x + 10°) = cos(2x + 20°), find the value of x (where x is acute).

Practice 9medium

Given that cos(24°) = p, express sin(66°) in terms of p.

Practice 10medium

If cot(47°) = q, what is tan(43°) equal to?

Practice 11medium

If sec(37°) = r, then cosec(53°) equals:

Practice 12medium

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

Practice 13medium

Simplify: sin²(18°) + sin²(72°)

Practice 14medium

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

Practice 15hard

If cos(3x − 15°) = sin(2x + 35°) and 0° < x < 90°, find the value of sin(x) + cos(x).

Practice 16hard

A ladder leans against a wall such that it makes an angle θ with the ground. If the angle between the ladder and the wall is (90° − θ), and the ladder is 10 m long, find the height on the wall in terms of sin(θ).

Practice 17hard

Given that sec(α) · sin(90° − α) = k, and α is an acute angle, express k in terms of tan(α).

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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