Trigonometry Questions For SSC CGL 2025, Solve Important Questions

The quantitative aptitude section is one of the most challenging parts of the exam. To score well, consistent practice across all key topics is essential. Trigonometry Questions for SSC CGL is an important topic you must prepare thoroughly for the upcoming exam. To help you with this, we have created a blog covering the 30 most important Trigonometry questions for the SSC CGL exam. Attempt these and assess your preparation level.

Common Mistakes Students Make While Attempting Trigonometry Questions

Understanding trigonometry concepts is important, but many students lose marks due to simple avoidable errors. Below are some of the common mistakes students make during exams:

1. Misapplying Trigonometric Identities
   Students often confuse identities like sin²θ + cos²θ = 1 or sec²θ – tan²θ = 1. One small error here can change the entire answer.
2. Incorrect Value Substitution
   Mistakes are common while substituting standard values such as sin 30°, cos 60°, or tan 45°. These values should be memorized properly.
3. Wrong Angle Unit Interpretation
   Mixing degrees and radians, especially in questions involving π, is a major source of error. Always check the unit before solving.
4. Ignoring Angle Conditions
   Questions often mention whether the angle is acute, obtuse, or between 0° and 90°. Ignoring this can lead to incorrect quadrant signs.
5. Skipping Basic Diagrams or Triangle Logic
   In geometry-based trigonometry, not drawing triangles or ignoring Pythagorean relationships (like a² + b² = c²) leads to confusion.
6. Calculation and Sign Errors
   Small calculation slips, especially in fractions and roots (like √3 or 1/2), can cause incorrect final answers even if the method is right.
7. Not Revising Formulas Thoroughly
   Lack of regular revision causes confusion between formulas like tan²θ = sec²θ – 1 and cot²θ = cosec²θ – 1.

Tips and Tricks to Solve Trigonometry Questions Quickly

Here are some useful tips and tricks to help you solve trigonometry questions faster and more accurately in exams like SSC CGL, SSC CHSL, and Railway Exams:

1. Memorize Standard Trigonometric Values

Know the values of sin, cos, tan, cosec, sec, and cot for key angles (0°, 30°, 45°, 60°, 90°) by heart.
Example table:

• sin 30° = 1/2
• cos 60° = 1/2
• tan 45° = 1

2. Use Trigonometric Identities Smartly

Common identities you must remember:

• sin²θ + cos²θ = 1
• 1 + tan²θ = sec²θ
• 1 + cot²θ = cosec²θ
  Apply these identities directly when you see matching expressions.

3. Convert All Angles to Degrees or Radians

Be consistent with units. If a question has π terms, convert them to degrees unless specifically asked in radians.

4. Use Complementary Angle Identities

Remember:

• sin(90° – θ) = cos θ
• tan(90° – θ) = cot θ
  These are helpful when angles add up to 90°.

5. Know the Signs of Ratios in All Four Quadrants (ASTC Rule)

• All positive in 1st quadrant (0° to 90°)
• Sin positive in 2nd quadrant (90° to 180°)
• Tan positive in 3rd quadrant (180° to 270°)
• Cos positive in 4th quadrant (270° to 360°)

Also check SSC CGL Maths Syllabus

6. Try Elimination in MCQs

If stuck, plug in answer options in the equation. It may save time rather than solving the full expression.

7. Break Down Complex Expressions

Simplify expressions like (1 – sin²θ) as cos²θ or (sec²θ – 1) as tan²θ to reduce steps.

8. Use Triangle-Based Visualization

For questions involving right-angled triangles, draw a triangle and use a:b:c ratios (like 3:4:5) to solve faster.

9. Practice Frequently Asked Patterns

Trigonometry often repeats question types. Practice questions like:

• Value-based simplification
• Trigonometric equation solving
• Triangle-based angle identification

10. Attempt Mock Tests Regularly

Mock tests help build speed and improve accuracy. Review your mistakes to strengthen weak areas. By applying these tricks, you’ll save time and reduce errors in the trigonometry section of competitive exams.

Practice Trigonometry Questions for SSC Exams

Solve these important Trigonometry MCQs to improve your chances in upcoming SSC exams. These questions are based on exam trends and include identities, values, and standard angles.

Q1. If sin A = 3/5 and A is acute, what is the value of cos A?
A) 4/5
B) 3/4
C) 5/3
D) 5/4
Correct Answer: A) 4/5

Q2. The value of sin² 60° + cos² 30° is
A) 1
B) 1.5
C) √3
D) 0
Correct Answer: B) 1.5

Q3. If tan A = 1, then the value of sin A + cos A is
A) √2
B) 1
C) √3
D) 2
Correct Answer: A) √

Q4. The value of sin² 45° + cos² 45° is
A) 1
B) 0
C) √2
D) 2
Correct Answer: A) 1

Q5. What is the value of tan 60° – cot 30°?
A) 0
B) 1
C) √3
D) 2√3
Correct Answer: A) 0

Q6. If A + B = 90°, then tan A × tan B =
A) 1
B) 0
C) –1
D) 2
Correct Answer: A) 1

Q7. The value of sec² θ – tan² θ is
A) 1
B) 0
C) 2
D) –1
Correct Answer: A) 1

Q8. If sin θ = 12/13, then what is cot θ?
A) 5/12
B) 12/5
C) 13/12
D) 12/13
Correct Answer: A) 5/12

Q9. If tan θ = 3/4, then what is sin θ?
A) 3/5
B) 4/5
C) 5/3
D) 5/4
Correct Answer: A) 3/5

Q10. What is the value of sin 30° × cos 60° + cos 30° × sin 60°?
A) 1
B) 0
C) √3
D) 1/2
Correct Answer: A) 1

Q11. sin 18° × sin 72° + cos 18° × cos 72° =
A) cos 54°
B) 1
C) 0
D) √2
Correct Answer: A) cos 54°

Q12. If cos A = 0.6, then tan A is
A) 3/4
B) 4/3
C) 5/4
D) 3/5
Correct Answer: B) 4/3

Q13. What is the value of sin 60° × sin 30° + cos 60° × cos 30°?
A) 1
B) √3
C) √3/2
D) 1/2
Correct Answer: C) √3/2

Q14. If cot θ = √3, then θ =
A) 60°
B) 30°
C) 45°
D) 0°
Correct Answer: B) 30°

Q15. The value of sin² 30° + sin² 60° is
A) 1
B) 3/4
C) 5/4
D) 2
Correct Answer: A) 1

Q16. tan² θ – sin² θ is equal to
A) sec²θ–1–sin²θ
B) cot² θ
C) cos² θ
D) 1
Correct Answer: A) sec²θ–1–sin²θ

Q17. The value of cosec² A – cot² A is
A) 1
B) 0
C) –1
D) 2
Correct Answer: A) 1

Q18. The angle whose cotangent is 1 is
A) 45°
B) 30°
C) 60°
D) 90°
Correct Answer: A) 45°

Q19. If sec A = 13/12, find tan A.
A) 5/12
B) 12/5
C) 13/5
D) 5/13
Correct Answer: A) 5/12

Q20. The maximum value of sin θ + cos θ is
A) √2
B) 1
C) 2
D) 0
Correct Answer: A) √2

Q21. sin² A + cos² A =
A) 1
B) 0
C) 2
D) 3
Correct Answer: A)

Q22. If tan θ = 1/√3, then θ =
A) 30°
B) 45°
C) 60°
D) 90°
Correct Answer: A) 30°

Q23. The value of sin 90° + cos 0° is
A) 2
B) 1
C) 0
D) √2
Correct Answer: A) 2

Q24. The value of (1 + tan² A)/(1 + cot² A) is
A) tan² A / cot² A
B) cot² A / tan² A
C) tan² A
D) 1
Correct Answer: C) tan² A

Q25. If sin θ = cos θ, then θ =
A) 30°
B) 45°
C) 60°
D) 90°
Correct Answer: B) 45

Q26. Which of the following is equal to sec² θ – tan² θ?
A) 1
B) 0
C) sin² θ
D) cos² θ
Correct Answer: A) 1

Q27. What is the value of sin 60° – sin 30°?
A) (√3–1)/2
B) 1/2
C) 1
D) 0
Correct Answer: A) (√3–1)/2

Q28. If A is acute and sin A = 5/13, find cos A.
A) 12/13
B) 13/5
C) 5/12
D) 1/2
Correct Answer: A) 12/13

Q29. If A = 45°, what is the value of tan² A – sec² A?
A) –1
B) 0
C) 1
D) 2
Correct Answer: A) –1

Q30. The value of sin 30° × cos 60° + cos 30° × sin 60° is
A) 1
B) 1/2
C) 0
D) √3/2
Correct Answer: A) 1

Also attempt SSC CGL Practice Quiz

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