7 questions from actual SSC GD Constable papers · all shown free · click option to reveal solution
In a right triangle, trigonometric ratios connect an angle with the ratios of two sides. For any angle θ (theta), there are six basic ratios: sine, cosine, tangent, cosecant, secant, and cotangent
Consider a right triangle with angle θ. The three sides are: Hypotenuse (longest side, opposite to 90°), Opposite (side facing angle θ), and Adjacent (side next to angle θ)
sin θ = Opposite/Hypotenuse cos θ = Adjacent/Hypotenuse tan θ = Opposite/Adjacent cosec θ = 1/sin θ = Hypotenuse/Opposite sec θ = 1/cos θ = Hypotenuse/Adjacent cot θ = 1/tan θ = Adjacent/Opposite Fundamental Identity: sin²θ + cos²θ = 1 (Most important for SSC CGL) Other Identities: 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ
SSC CGL asks direct ratio calculations, value finding, and identity-based problems. Questions often involve standard angles (0°, 30°, 45°, 60°, 90°) and basic identities. Shortcut #1 - Standard Angle Values: For 0°, 30°, 45°, 60°, 90°: sin values: 0, 1/2, 1/√2, √3/2, 1 cos values: 1, √3/2, 1/√2, 1/2, 0 tan values: 0, 1/√3, 1, √3, undefined Memory trick: sin 30° = 1/2, sin 60° = √3/2 (opposite values for cos)
Use identity sin²θ + cos²θ = 1
(3/5)² + cos²θ = 1
9/25 + cos²θ = 1
cos²θ = 1 - 9/25 = 16/25
cos θ = 4/5 (taking positive value)
tan θ = sin θ/cos θ = (3/5)/(4/5) = 3/4 Answer: cos θ = 4/5, tan θ = 3/4 Shortcut #2 - Quick Identity Check: Whenever given one ratio, immediately use sin²θ + cos²θ = 1 to find others. This saves calculation time in exams. Worked Example 2: Simplify (sin θ × cosec θ) + (cos θ × sec θ)
Replace cosec θ = 1/sin θ and sec θ = 1/cos θ
(sin θ × 1/sin θ) + (cos θ × 1/cos θ)
1 + 1 = 2 Answer: 2 Shortcut #3 - Reciprocal Recognition: Instantly recognize reciprocal pairs: sin-cosec, cos-sec, tan-cot. Their product always equals 1.
#1: Students often confuse opposite and adjacent sides when angle position changes. Always identify the angle first, then mark opposite and adjacent accordingly. Many students lose marks by mixing up sin and cos definitions when the triangle orientation changes.
Practice identifying sides relative to the given angle, not the triangle's position on paper. Practical Exam Tip: In multiple choice questions, if you get values like sin θ = 4/3 or cos θ = 6/5, immediately mark it wrong. Sine and cosine values cannot exceed 1. This elimination technique saves precious exam time.