NOTES FOR CLASS 11 | CH 10 ALL FORMULAS

Class 11 Mathematics – Punjab Board
Chapter 10: Trigonometric Identities
Formulae (Exercise-wise)
Exercise 10.1 (Fundamental Law of Trigonometry)
 cos(A - B) = cos A cos B + sin A sin B
 cos(A + B) = cos A cos B - sin A sin B
 sin(A + B) = sin A cos B + cos A sin B
 sin(A - B) = sin A cos B - cos A sin B
 cos(2A) = cos²A - sin²A = 2cos²A - 1 = 1 - 2sin²A
 sin(2A) = 2 sin A cos A
 sin²θ + cos²θ = 1
 1 + tan²θ = sec²θ
 1 + cot²θ = csc²θ


Exercise 10.2 (Allied Angles)
 sin(90° - θ) = cos θ, sin(90° + θ) = cos θ
 sin(180° - θ) = sin θ, sin(180° + θ) = -sin θ
 sin(270° + θ) = -cos θ, sin(360° - θ) = -sin θ
 cos(90° - θ) = sin θ, cos(90° + θ) = -sin θ
 cos(180° - θ) = -cos θ, cos(180° + θ) = -cos θ
 cos(270° + θ) = sin θ, cos(360° - θ) = cos θ
 tan(90° - θ) = cot θ, tan(90° + θ) = -cot θ
 tan(180° + θ) = tan θ, tan(270° + θ) = -cot θ, tan(360° - θ) = -tan θ
 cot(90° ± θ) = tan θ, sec(90° ± θ) = csc θ, csc(90° ± θ) = sec θ
 sin(-θ) = -sin θ, cos(-θ) = cos θ, tan(-θ) = -tan θ


Exercise 10.3 (Sum, Difference & Multiple Angles)
 sin(A + B) = sin A cos B + cos A sin B
 sin(A - B) = sin A cos B - cos A sin B
 cos(A + B) = cos A cos B - sin A sin B
 cos(A - B) = cos A cos B + sin A sin B
 sin(2θ) = 2 sin θ cos θ
 cos(2θ) = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ
 tan(2θ) = (2 tan θ)/(1 - tan²θ)
 sin(3θ) = 3 sin θ - 4 sin³θ
 cos(3θ) = 4 cos³θ - 3 cos θ