SSC CGL Quant – Trigonometry – Level 2 · Exam Level · Tier I Sprint

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SSC CGL Quant – Trigonometry – Level 2 · Exam Level · Tier I Sprint – 15 questions, subject: Quantitative Aptitude. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
If sin θ = 8/17 (θ acute), then sec θ + tan θ equals:

Correct Answer: B [5/3]

Explanation:

8-15-17: sec = 17/15, tan = 8/15 → 25/15 = 5/3.

2.  
The value of tan 5° × tan 25° × tan 45° × tan 65° × tan 85° is:

Correct Answer: C [1]

Explanation:

tan 5° tan 85° = 1, tan 25° tan 65° = 1, tan 45° = 1.

3.  
If cos θ = 3/5 (θ acute), then sin θ + tan θ equals:

Correct Answer: A [32/15]

Explanation:

sin = 4/5, tan = 4/3 → 12/15 + 20/15 = 32/15.

4.  
If sec θ − tan θ = 1/4, then cos θ equals:

Correct Answer: D [8/17]

Explanation:

sec + tan = 4; sec = (4 + 1/4)/2 = 17/8 → cos = 8/17.

5.  
If sin θ + cos θ = √2 and θ is acute, then tan θ + cot θ equals:

Correct Answer: D [2]

Explanation:

Only θ = 45° gives √2 → 1 + 1 = 2.

6.  
(1 + cot² θ)(1 − cos² θ) simplifies to:

Correct Answer: A [1]

Explanation:

cosec² θ × sin² θ = 1.

7.  
From a point 40√3 m from the foot of a tower, the angle of elevation of its top is 30°. The height of the tower is:

Correct Answer: B [40 m]

Explanation:

h = 40√3 × tan 30° = 40 m.

8.  
From the top of a 60 m cliff, the angle of depression of a car on the road is 60°. How far is the car from the foot of the cliff?

Correct Answer: C [20√3 m]

Explanation:

Distance = 60 / tan 60° = 60/√3 = 20√3 m.

9.  
Two-quantity comparison
Quantity I: sin² 60° + cos² 45°
Quantity II: tan² 30° + sec² 45° − 1

Correct Answer: B [Quantity I < Quantity II]

Explanation:

QI = 3/4 + 1/2 = 5/4; QII = 1/3 + 2 − 1 = 4/3 → QI < QII.

10.  
Trick SpotterIf sec θ + tan θ = 7, which is the fastest correct way to get sec θ?

Correct Answer: B [sec θ − tan θ = 1/7, so sec θ = (7 + 1/7)/2 = 25/7]

Explanation:

Because (sec + tan)(sec − tan) = 1, add the pair and halve: 25/7.

11.  
Spot My Mistake“From the top of a 30 m tower the angle of depression of a car is 30°, so the car is 30 tan 30° = 10√3 m away.” The correct distance is:

Correct Answer: D [30√3 m]

Explanation:

Distance = height ÷ tan 30° = 30 × √3 = 30√3 m; tan is P/B, not B/P.

12.  
Diagram-basedIn the figure, the angle of elevation of the top of a tower of height 15√3 m is 60°. Find d.

Correct Answer: A [15 m]

Explanation:

d = 15√3 / tan 60° = 15√3/√3 = 15 m.

13.  
A wheel turns through 7π/12 radians. This angle in degrees is:

Correct Answer: C [105°]

Explanation:

7/12 × 180° = 105°.

14.  
cos² θ / (1 − sin θ) is equal to:

Correct Answer: A [1 + sin θ]

Explanation:

cos² θ = (1 − sin θ)(1 + sin θ); cancel (1 − sin θ).

15.  
Reverse questionθ is acute, θ > 45° and sin θ × cos θ = √3/4. What is tan θ?

Correct Answer: D [√3]

Explanation:

sin 2θ = √3/2 → 2θ = 60° or 120° → θ = 30° or 60°; θ > 45° → θ = 60°, tan θ = √3.

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Quantitative Aptitude book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-quantitative-aptitude

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