JEE Main Maths · Trigonometry PYQ
JEE Main Trigonometry Previous Year Questions (2002–2025)
Trigonometry is tied with Calculus chapters for the highest weightage in JEE Main Mathematics — ~8% with 2 questions per paper consistently. It combines Trigonometric equations, Inverse Trig, Heights & Distances and Properties of Triangles into one dense chapter that rewards identity mastery.
Trigonometry PYQs from 2002 to 2025, tagged by sub-topic and difficulty. Every solution uses KaTeX-rendered math and identifies the core identity or technique up front.
Trigonometry (including Inverse) at a Glance
Key Sub-Topics & What's Tested
Trigonometric Identities
Pythagorean, reciprocal, quotient, compound-angle, double-angle, half-angle, product-to-sum, sum-to-product identities.
Trigonometric Equations
Solving sin x = k, cos x = k, tan x = k types, general solutions, finding specific solutions within given interval.
Inverse Trigonometric Functions
Principal value branches, identities (sin⁻¹ + cos⁻¹ = π/2), differentiation results, derivations using right triangles.
Heights & Distances
Angle of elevation/depression, problems on towers, ships, aircraft, using law of sines/cosines in practical problems.
Properties of Triangles
Law of sines (a/sin A = b/sin B = c/sin C = 2R), law of cosines, area formulas (½ab sin C, rs, abc/4R), half-angle formulas.
Sum/Difference Formulas
sin(A±B), cos(A±B), tan(A±B), triple-angle formulas, sin 3θ = 3 sin θ - 4 sin³θ etc.
Maximum/Minimum Values
Max/min of a sin x + b cos x = ±√(a² + b²), a cos x + b sin x + c — common JEE PYQ template.
Trigonometric Series
Sum of sin and cos series (telescopic), C+iS formulas using complex numbers for trigonometric series.
Question Type Distribution
| Question Type | Share (approx) | Example Pattern |
|---|---|---|
| Identity Proofs / Simplification | 20% | Simplify (sin 3θ + sin θ) / (cos 3θ + cos θ). |
| Equation Solving | 20% | Find number of solutions of sin x + cos x = 1 in [0, 2π]. |
| Inverse Trig Problems | 20% | Find sin⁻¹(sin 3π/4) — express in principal value range. |
| Properties of Triangles | 15% | In triangle ABC, if a = 3, b = 4, c = 5, find area using law of cosines. |
| Heights & Distances | 10% | From top of tower 50m, angle of depression of object is 30° — find distance. |
| Max/Min Values | 15% | Find maximum value of 3 sin x + 4 cos x + 5. |
How to Solve Trigonometry (including Inverse) PYQs
- 1Lock the 20 key identities. Pythagorean, double-angle, half-angle, product-to-sum, sum-to-product. Without instant recall, identity-based PYQs waste 3 minutes each.
- 2For equations, general solution first. sin x = k → x = nπ + (-1)ⁿ·arcsin(k). cos x = k → x = 2nπ ± arccos(k). tan x = k → x = nπ + arctan(k). Master these three formulas.
- 3Inverse trig: respect principal value branches. sin⁻¹ ∈ [-π/2, π/2], cos⁻¹ ∈ [0, π], tan⁻¹ ∈ (-π/2, π/2). Applying outside these ranges breaks the answer.
- 4For triangle problems, use law of sines first. Given two angles and one side, law of sines handles it in one step. Law of cosines for two sides and included angle.
- 5For max/min of a sin x + b cos x, use √(a² + b²) form. Max = √(a² + b²), min = -√(a² + b²). Direct shortcut — no calculus needed.
Common Mistakes That Cost Marks
- Wrong quadrant assignment. sin⁻¹(sin 3π/4) ≠ 3π/4. Since 3π/4 is outside principal range, adjust to π - 3π/4 = π/4.
- Forgetting multiple solutions in given interval. sin x = 1/2 in [0, 2π] has TWO solutions (π/6 and 5π/6), not one.
- Using radians when degrees are expected (or vice versa). JEE typically uses radians for algebraic problems, degrees for heights & distances. Watch units.
- Confusing angle of elevation vs depression. Elevation: looking up from ground to object. Depression: looking down from height. Swapping changes the answer.
- Wrong sign in triple-angle formulas. sin 3θ = 3 sin θ - 4 sin³θ. cos 3θ = 4 cos³θ - 3 cos θ. Mix up the signs and the answer flips.
Related JEE Main Practice
Frequently asked questions
How many Trigonometry PYQs should I solve?
Target 80–100 PYQs across 2010–2025. At ~8% weightage among the highest in Maths, Trigonometry deserves over-practice. Identity-heavy PYQs reward pattern recognition built through volume.
Is Trigonometry harder in JEE Main or JEE Advanced?
JEE Advanced. Main tests identity manipulation and standard problems. Advanced introduces more intricate equation solving and multi-step inverse trig proofs. Master Main first.
Do I need to memorise all 20 identities?
Yes — at least the 15 core ones (Pythagorean, reciprocal, compound-angle, double-angle, half-angle, product-to-sum). Without fluent recall, PYQs take 3× longer.
What's the most-tested Inverse Trig PYQ template?
Converting sin⁻¹ or cos⁻¹ or tan⁻¹ of an angle outside principal range into principal form. Appears in 3–4 PYQs per 10-year window.
How do I approach max/min without calculus?
For a sin x + b cos x, max = √(a² + b²). For more complex expressions, rewrite using identities first. Only use calculus for non-standard expressions.
Are Heights & Distances PYQs formulaic?
Mostly yes — practical problems reducing to right triangle trigonometry. Common templates: tower with angle of elevation from two points, aircraft moving horizontally observed from ground.
Start Trigonometry PYQs free
One of the highest-weightage Maths chapters. Chapter-wise PYQs on identities, equations, inverse trig and properties of triangles. Sign in in 30 seconds.
Start Free Practice