Study Material — 7 PYQs (2021–2021) · Concept Notes · Shortcuts
SSC GD Constable Basic Trig Ratios is a frequently tested subtopic — 7 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.
In a right triangle, if tan θ = 5/12, what is the value of sec θ?
Exam Q 42021Previous Year Pattern
If cos θ = 5/13 and sin θ > 0, find the value of (tan θ × sec θ).
Exam Q 52021Previous Year Pattern
In a right triangle, if cot θ = 8/15, find the value of sin θ.
Exam Q 62021Previous Year Pattern
If tan θ = √3 and θ is in the first quadrant, find the value of (sin³ θ − cos³ θ)/(sin θ − cos θ).
Exam Q 72021Previous Year Pattern
If sin θ − cos θ = 1/5, find the value of sin θ cos θ.
Concept Notes
Basic Trig Ratios— Rules & Concept
💡
Core Concept
Read this first — the foundation of the topic
→Core Concept
In a right triangle, trigonometric ratios connect an angle with the ratios of two sides. For any angle θ (theta), there are six basic ratios: sine, cosine, tangent, cosecant, secant, and cotangent
💡Key Definitions
Consider a right triangle with angle θ. The three sides are: Hypotenuse (longest side, opposite to 90°), Opposite (side facing angle θ), and Adjacent (side next to angle θ)
→Basic Ratios
sin θ = Opposite/Hypotenuse
cos θ = Adjacent/Hypotenuse
tan θ = Opposite/Adjacent
cosec θ = 1/sin θ = Hypotenuse/Opposite
sec θ = 1/cos θ = Hypotenuse/Adjacent
cot θ = 1/tan θ = Adjacent/Opposite
Fundamental Identity: sin²θ + cos²θ = 1 (Most important for SSC CGL)
Other Identities: 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ
📊
Exam Patterns
What examiners ask — read before attempting PYQs
✏️Worked Example 2
1
Replace cosec θ = 1/sin θ and sec θ = 1/cos θ
2
(sin θ × 1/sin θ) + (cos θ × 1/cos θ)
3
1 + 1 = 2
Answer: 2
Shortcut #3 - Reciprocal Recognition:
Instantly recognize reciprocal pairs: sin-cosec, cos-sec, tan-cot. Their product always equals 1.
Common Mistake #1: Students often confuse opposite and adjacent sides when angle position changes. Always identify the angle first, then mark opposite and adjacent accordingly. Many students lose marks by mixing up sin and cos definitions when the triangle orientation changes. Practice identifying sides relative to the given angle, not the triangle's position on paper
💡Practical Exam Tip
In multiple choice questions, if you get values like sin θ = 4/3 or cos θ = 6/5, immediately mark it wrong. Sine and cosine values cannot exceed 1. This elimination technique saves precious exam time.
Key Points to Remember
sin θ = Opposite/Hypotenuse, cos θ = Adjacent/Hypotenuse, tan θ = Opposite/Adjacent
cosec θ, sec θ, cot θ are reciprocals of sin θ, cos θ, tan θ respectively
Fundamental identity: sin²θ + cos²θ = 1 (appears in 80% of trigonometry questions)
Standard angles: sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2
cos 30° = √3/2, cos 45° = 1/√2, cos 60° = 1/2
tan 30° = 1/√3, tan 45° = 1, tan 60° = √3
Quick check: sin θ and cos θ values must always be between -1 and 1