Example 1
What is the value of sin²θ + cos²θ?
Answer: A) 1
This is the basic Pythagorean identity.
Trigonometry questions for competitive exams: rules, worked examples and practice
Trigonometry questions use standard angle values and identities. Memorising the table for 0°, 30°, 45°, 60° and 90° solves most of them.
Key rules and formulas
- sin²θ + cos²θ = 1; sec²θ − tan²θ = 1; cosec²θ − cot²θ = 1.
- sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2; cos values reverse that order.
- tan 45° = 1, tan 30° = 1/√3, tan 60° = √3.
- sin(90° − θ) = cos θ; tan(90° − θ) = cot θ.
Common traps
- Swapping the sin and cos values for 30° and 60°.
- Sign errors with sec² − tan² (it equals 1, not −1).
Where Trigonometry is asked
- SSC CGL Tier 1 (Quantitative Aptitude)
- SSC CHSL Tier 1 (Quantitative Aptitude)
Worked examples
Example 2
What is the value of 2 sin 45° cos 45°?
Answer: A) 1
2 sin θ cos θ = sin 2θ = sin 90° = 1.
Frequently asked questions
What is Trigonometry in competitive exams?
Trigonometry questions use standard angle values and identities. Memorising the table for 0°, 30°, 45°, 60° and 90° solves most of them.
Which exams ask Trigonometry questions?
On MockBazaar, Trigonometry questions appear in SSC CGL Tier 1, SSC CHSL Tier 1.
What is the most common mistake in Trigonometry?
Swapping the sin and cos values for 30° and 60°.