For ECET 2026 aspirants, Mathematics is a core subject that determines your rank. One of the most tested areas is Trigonometric Identities, which forms the foundation for solving many types of problems in geometry, calculus, and coordinate systems. Mastering these identities not only helps with direct questions but also simplifies complex problems in other chapters. Let’s revise the key formulas and practice 10 ECET-style MCQs with answers and explanations.
📘 Concept Notes – Trigonometric Identities
🔹 What Are Trigonometric Identities?
Trigonometric identities are equalities involving trigonometric functions that are true for all values of the variables involved (within the domain of definition). These identities help simplify and solve trigonometric equations efficiently.
✅ Basic Trigonometric Ratios
| Ratio | Formula |
|---|---|
| sin θ | Opposite / Hypotenuse |
| cos θ | Adjacent / Hypotenuse |
| tan θ | Opposite / Adjacent = sin θ / cos θ |
| cot θ | 1 / tan θ = cos θ / sin θ |
| sec θ | 1 / cos θ |
| cosec θ | 1 / sin θ |
🔗 Fundamental Identities
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ
- 1 + cot²θ = cosec²θ
These are called Pythagorean identities.
🔁 Reciprocal Identities
- sin θ = 1 / cosec θ
- cos θ = 1 / sec θ
- tan θ = 1 / cot θ
🔄 Quotient Identities
- tan θ = sin θ / cos θ
- cot θ = cos θ / sin θ
✨ Complementary Angle Identities
- sin(90° − θ) = cos θ
- cos(90° − θ) = sin θ
- tan(90° − θ) = cot θ
- cot(90° − θ) = tan θ
- sec(90° − θ) = cosec θ
- cosec(90° − θ) = sec θ
🔢 Key Angle Values Table
| θ | sin θ | cos θ | tan θ |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | ∞ |
🔟 10 Most Expected MCQs – ECET 2026 [Trigonometric Identities]
Q1. What is the value of sin²θ + cos²θ?
A) 2
B) 1
C) sin θ
D) cos θ
Q2. Which identity is true?
A) tan²θ + 1 = cosec²θ
B) cot²θ − 1 = cosec²θ
C) tan²θ + 1 = sec²θ
D) sec²θ − 1 = tan θ
Q3. tan θ is equal to:
A) sin θ × cos θ
B) sin θ / cos θ
C) cos θ / sin θ
D) sec θ / cosec θ
Q4. If sin θ = 3/5, what is cos θ?
A) 4/5
B) 5/3
C) 1/2
D) 5/4
Q5. cot θ is reciprocal of:
A) sec θ
B) tan θ
C) cos θ
D) sin θ
Q6. If θ = 45°, then tan θ = ?
A) 0
B) 1
C) √3
D) 1/√3
Q7. Which of these is NOT a Pythagorean identity?
A) sin²θ + cos²θ = 1
B) tan²θ + 1 = sec²θ
C) cot²θ + 1 = cosec²θ
D) sec²θ − tan²θ = cosec²θ
Q8. sec²θ − tan²θ equals:
A) 1
B) tan θ
C) sec θ
D) 0
Q9. cos(90° − θ) equals:
A) sin θ
B) cos θ
C) tan θ
D) cot θ
Q10. sin θ × cosec θ equals:
A) tan θ
B) 1
C) sec θ
D) cos θ
✅ Answer Key Table
| Q.No | Answer |
|---|---|
| Q1 | B |
| Q2 | C |
| Q3 | B |
| Q4 | A |
| Q5 | B |
| Q6 | B |
| Q7 | D |
| Q8 | A |
| Q9 | A |
| Q10 | B |
🧠 Explanations of All Answers
- Q1 → B: sin²θ + cos²θ = 1 is a standard identity.
- Q2 → C: tan²θ + 1 = sec²θ is the correct Pythagorean identity.
- Q3 → B: tan θ = sin θ / cos θ by definition.
- Q4 → A: Use Pythagoras: cos θ = √(1 − sin²θ) = √(1 − 9/25) = 4/5.
- Q5 → B: cot θ = 1 / tan θ → reciprocal of tan.
- Q6 → B: tan 45° = 1 (standard angle identity).
- Q7 → D: sec²θ − tan²θ = 1, not equal to cosec²θ.
- Q8 → A: Derived identity: sec²θ − tan²θ = 1.
- Q9 → A: cos(90° − θ) = sin θ (complementary angle rule).
- Q10 → B: sin θ × cosec θ = sin θ × 1/sin θ = 1.
🎯 Why This Practice Matters for ECET 2026
Trigonometric identities are frequently tested in ECET, not only directly but also indirectly in coordinate geometry, integration, and differentiation. These are easy 1-mark questions if your formulas are strong. This topic is perfect for high accuracy and speed, helping students maximize their math score.
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