SSC CGL Quant – Trigonometry – Level 3 · Challenge

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SSC CGL Quant – Trigonometry – Level 3 · Challenge – 10 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 + cos θ = 17/13 (θ acute), then sin θ cos θ is:

Correct Answer: C [60/169]

Explanation:

(sin + cos)² = 1 + 2 sin cos → 289/169 − 1 = 120/169 → sin cos = 60/169.

2.  
If tan θ = 3/4 (θ acute), find (2 sin θ + 3 cos θ)/(4 cos θ − sin θ).

Correct Answer: B [18/13]

Explanation:

sin = 3/5, cos = 4/5 → (6/5 + 12/5)/(16/5 − 3/5) = 18/13.

3.  
Assertion–Reason
A: sin² 1° + sin² 2° + … + sin² 89° = 44.5
R: sin² θ + sin² (90° − θ) = 1

Correct Answer: C [Both A and R are true and R explains A]

Explanation:

44 pairs make 44, plus sin² 45° = ½ → 44.5; R is the pairing rule.

4.  
Two observers on the same side of a tower are 60 m apart. The angles of elevation of the top from them are 30° and 60°. The height of the tower is:

Correct Answer: A [30√3 m]

Explanation:

30-60 Ladder: h = (√3/2) × 60 = 30√3 m.

5.  
Two men on opposite sides of a 75 m tower see its top at angles of elevation 30° and 60°. How far apart are the men?

Correct Answer: B [100√3 m]

Explanation:

75√3 + 75/√3 = 75√3 + 25√3 = 100√3 m.

6.  
The shadow of a vertical pole is √3 times its height. The angle of elevation of the sun is:

Correct Answer: D [30°]

Explanation:

tan θ = h/(√3 h) = 1/√3 → θ = 30°.

7.  
sin⁴ θ − cos⁴ θ is equal to:

Correct Answer: B [2 sin² θ − 1]

Explanation:

(sin² − cos²)(sin² + cos²) = sin² θ − cos² θ = 2 sin² θ − 1.

8.  
True/False countHow many of these statements are true?
I. tan 1° × tan 89° = 1
II. cos 0° = sec 0°
III. sin 30° + sin 60° = sin 90°

Correct Answer: A [Only 2]

Explanation:

I true (complementary), II true (both 1), III false: ½ + √3/2 ≈ 1.37 ≠ 1.

9.  
The angles of elevation of the top of a tower from two points 9 m and 16 m from its foot, on the same straight line, are complementary. The height of the tower is:

Correct Answer: C [12 m]

Explanation:

tan α × tan β = (h/9)(h/16) = 1 → h² = 144 → h = 12 m.

10.  
The minimum value of sin² θ + cos⁴ θ is:

Correct Answer: D [3/4]

Explanation:

sin² θ + cos⁴ θ = (cos² θ − ½)² + ¾ → least value ¾ when cos² θ = ½.

➤ 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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