Trigonometry Questions for SSC CGL: What This Set Covers
This page has 20 original SSC-style trigonometry questions with solutions, grouped into the four patterns that SSC repeats most: standard values and complementary angles, identities and "sec θ + tan θ" type pairs, maximum and minimum values, and height and distance. The SSC CGL 2026 notice lists "Trigonometric ratio, Degree and Radian Measures, Standard Identities, Complementary angles, Heights and Distances" in the Tier 1 Quantitative Aptitude syllabus (para 13.10.3), and "Trigonometric ratios, Complementary angles, Height and distances (simple problems only)" in the Tier 2 Mathematical Abilities syllabus (para 13.11.1.6).
Why now: SSC CGL Tier 2 is tentatively in December 2026 and SSC CHSL Tier 1 runs 30 November–31 December 2026 (official SSC notices). Trigonometry questions are short once you know the identity, so they are the cheapest marks to add in the last month.
Keep Trigonometry Formulas for SSC CGL open for the values table; this page is the practice set.
The 8 Results These Questions Use
| Result | Use it when you see… |
|---|---|
| sin²θ + cos²θ = 1; sec²θ − tan²θ = 1; cosec²θ − cot²θ = 1 | Any simplification |
| (sec θ + tan θ)(sec θ − tan θ) = 1 | "If sec θ + tan θ = k…" |
| (cosec θ + cot θ)(cosec θ − cot θ) = 1 | "If cosec θ − cot θ = k…" |
| sin(90° − θ) = cos θ; tan(90° − θ) = cot θ | Angles adding to 90° |
| Max of a sin θ + b cos θ = √(a² + b²) | Maximum value questions |
| a sin²θ + b cos²θ lies between the smaller and larger of a and b | Range questions |
| tan²θ + cot²θ ≥ 2 | Minimum value questions |
| Height = distance × tan(angle of elevation) | Height and distance |
Set A: Values and Complementary Angles (Q1–Q5)
Q1. Find sin²30° + cos²60° + tan²45°. (a) 1 (b) 1.5 (c) 2 (d) 0.5 Answer: (b) 1.5. 1/4 + 1/4 + 1.
Q2. Find sin 25°/cos 65° + tan 20° tan 70°. (a) 0 (b) 1 (c) 2 (d) √3 Answer: (c) 2. sin 25° = cos 65°, and tan 20° tan 70° = tan 20° cot 20° = 1.
Q3. Find tan 1° tan 2° tan 3° … tan 89°. (a) 0 (b) 1 (c) 89 (d) √3 Answer: (b) 1. Pair tan θ with tan(90° − θ) = cot θ; the middle term tan 45° = 1.
Q4. Find sin²1° + sin²2° + … + sin²89°. (a) 44 (b) 44.5 (c) 45 (d) 89 Answer: (b) 44.5. 44 pairs of sin²θ + cos²θ = 1, plus sin²45° = 1/2.
Q5. Express 15° in radians. (a) π/6 (b) π/10 (c) π/12 (d) π/15 Answer: (c). 15 × π/180.
Set B: Identities and Pairs (Q6–Q12)
Q6. If sin θ = 3/5 and θ is acute, find tan θ + sec θ. (a) 1 (b) 7/4 (c) 2 (d) 9/4 Answer: (c) 2. cos θ = 4/5, so tan θ = 3/4 and sec θ = 5/4.
Q7. If sec θ + tan θ = 3, find sec θ. (a) 4/3 (b) 5/3 (c) 2 (d) 10/3 Answer: (b) 5/3. sec θ − tan θ = 1/3; adding, 2 sec θ = 10/3.
Q8. If cosec θ − cot θ = 1/4, find cosec θ. (a) 15/8 (b) 17/8 (c) 2 (d) 17/4 Answer: (b) 17/8. cosec θ + cot θ = 4; adding, 2 cosec θ = 17/4.
Q9. Simplify (1 − sin²θ) sec²θ. (a) 0 (b) 1 (c) tan²θ (d) sin²θ Answer: (b) 1. cos²θ × sec²θ.
Q10. Find (sin θ + cos θ)² + (sin θ − cos θ)². (a) 0 (b) 1 (c) 2 (d) 4 sin θ cos θ Answer: (c) 2. The 2 sin θ cos θ terms cancel; 2(sin²θ + cos²θ).
Q11. If sin θ + sin²θ = 1, find cos²θ + cos⁴θ. (a) 0 (b) 1 (c) 2 (d) 1/2 Answer: (b) 1. sin θ = 1 − sin²θ = cos²θ, so cos²θ + cos⁴θ = sin θ + sin²θ = 1.
Q12. If sin θ + cos θ = √2 cos θ, then cos θ − sin θ equals: (a) √2 cos θ (b) √2 sin θ (c) sin θ (d) 1 Answer: (b). From the given, sin θ = (√2 − 1) cos θ, so cos θ − sin θ = (2 − √2) cos θ = √2 (√2 − 1) cos θ = √2 sin θ.
Set C: Maximum, Minimum and Equations (Q13–Q16)
Q13. Find the maximum value of 3 sin θ + 4 cos θ. (a) 3 (b) 4 (c) 5 (d) 7 Answer: (c) 5. √(9 + 16). Trap: 7 is the sum, not the maximum.
Q14. Find the minimum value of 9 sin²θ + 16 cos²θ. (a) 7 (b) 9 (c) 12.5 (d) 16 Answer: (b) 9. It equals 9 + 7 cos²θ, smallest when cos θ = 0.
Q15. Find the minimum value of tan²θ + cot²θ. (a) 0 (b) 1 (c) 2 (d) 4 Answer: (c) 2. By AM ≥ GM, since tan²θ × cot²θ = 1.
Q16. If sin(A + B) = 1 and cos(A − B) = √3/2, with A > B and both acute, find A and B. (a) 60°, 30° (b) 45°, 45° (c) 75°, 15° (d) 50°, 40° Answer: (a). A + B = 90°, A − B = 30°.
Set D: Height and Distance (Q17–Q20)
Q17. From a point 20 m from the foot of a tower, the angle of elevation of its top is 60°. Find the height. (a) 20 m (b) 20√3 m (c) 40 m (d) 10√3 m Answer: (b). h = 20 tan 60°.
Q18. When the sun's elevation is 30°, how long is the shadow of a 10 m pole? (a) 10 m (b) 10√3 m (c) 20 m (d) 10/√3 m Answer: (b). Shadow = 10 cot 30° = 10√3.
Q19. A 10 m ladder makes an angle of 60° with the ground. How high up the wall does it reach? (a) 5 m (b) 5√3 m (c) 10√3 m (d) 5√2 m Answer: (b). 10 sin 60°.
Q20. From two points on the same side of a tower and in line with it, the angles of elevation of the top are 30° and 60°. The points are 40 m apart. Find the height of the tower. (a) 20 m (b) 20√3 m (c) 40 m (d) 40√3 m Answer: (b). Distance = h(cot 30° − cot 60°) = h(√3 − 1/√3) = 2h/√3, so 40 = 2h/√3.
Shortcut for Q20: with 30° and 60° from the same side, the tower height is always (√3/2) × the gap between the points.
Answer Key
| Q | Ans | Q | Ans | Q | Ans | Q | Ans |
|---|---|---|---|---|---|---|---|
| 1 | b | 6 | c | 11 | b | 16 | a |
| 2 | c | 7 | b | 12 | b | 17 | b |
| 3 | b | 8 | b | 13 | c | 18 | b |
| 4 | b | 9 | b | 14 | b | 19 | b |
| 5 | c | 10 | c | 15 | c | 20 | b |
Practise Under Time
- SSC CGL trigonometry mock test 01, 02, 03
- Mixed maths: SSC CGL Tier 1 mock: Geometry and Coordinate Geometry
- Next set: Algebra questions for SSC CGL, Geometry questions for SSC CGL
Trigonometry Questions FAQs
How do I solve "sec θ + tan θ = k" questions quickly?
Use (sec θ + tan θ)(sec θ − tan θ) = 1, so sec θ − tan θ = 1/k. Add or subtract the two equations to get sec θ or tan θ.
What is the maximum value of a sin θ + b cos θ?
√(a² + b²). For 3 sin θ + 4 cos θ it is 5; the minimum is −5.
Is height and distance asked in SSC CGL Tier 1?
Yes. The SSC CGL 2026 notice lists "Heights and Distances" in the Tier 1 syllabus and "Height and distances (simple problems only)" in the Tier 2 syllabus.
Do I need radian measure for SSC CGL?
The Tier 1 syllabus in the 2026 notice includes "Degree and Radian Measures", so learn the conversion: radians = degrees × π/180.
How many trigonometry questions come in SSC CGL?
SSC does not publish topic-wise counts. Trigonometry is part of the Quantitative Aptitude syllabus in Tier 1 and Mathematical Abilities in Tier 2.
Practice Next for SSC Maths
- Formulas: Trigonometry formulas, Height and distance, Algebra formulas
- Plans: SSC CGL Tier 2 preparation strategy 2026, SSC CHSL preparation strategy 2026
Sources: SSC CGL 2026 notice (syllabus paras 13.10 and 13.11); SSC notice dated 01.10.2026. Questions and solutions are original BookOfExams material. Last checked 7 November 2026.