Trigonometry – JEE Mains Mathematics

• by Zenith LMS
• Updated April 2025

1. Trigonometric Functions

• Basic ratios: sin, cos, tan, cot, sec, cosec.
• Relation between trigonometric ratios.
• Trigonometric functions of standard angles: 0°, 30°, 45°, 60°, 90°.
• Signs of trigonometric functions in different quadrants (ASTC rule).
• Periodicity, domain, and range of functions.
• Graphs of sine, cosine, and tangent functions.

2. Trigonometric Identities

• Pythagorean Identities:

  sin²θ + cos²θ = 1

  1 + tan²θ = sec²θ

  1 + cot²θ = cosec²θ

• Sum and Difference Formulas:

  sin(A ± B) = sinA cosB ± cosA sinB

  cos(A ± B) = cosA cosB ∓ sinA sinB

  tan(A ± B) = (tanA ± tanB) / (1 ∓ tanA tanB)

• Double Angle Formulas:

  sin(2A) = 2sinA cosA

  cos(2A) = cos²A - sin²A

  tan(2A) = 2tanA / (1 - tan²A)

• Product to Sum and Sum to Product Formulas

3. Inverse Trigonometric Functions

• Definition and principal value branch.
• Domains and ranges of inverse trigonometric functions.
• Properties and identities:

  sin⁻¹x + cos⁻¹x = π/2

  tan⁻¹x + cot⁻¹x = π/2

  2tan⁻¹x = sin⁻¹(2x / (1 + x²))

• Graphs of inverse functions.

4. Applications in Geometry

• Solving triangles using sine rule and cosine rule.
• Area of triangle using trigonometry:

  Area = (1/2)ab sinC

• Height and distance problems using trigonometric ratios.