Trigonometric Identities

Trigonometric Identities

1. Basic Trigonometric Identities

   • Reciprocal and Quotient Identities
     • sec(x) = 1/cos(x), csc(x) = 1/sin(x), cot(x) = 1/tan(x) cot(x)= cos(x)/sin(x), tan(x) = sin(x)/cos(x)
   • Pythagorean Identities
     • sin2(t) + cos2(t) = 1 tan2(t) + 1 = sec2(t) 1 + cot2(t) = csc2(t)

2. Addition and Substraction Identities

   • Sum and Difference formulas for Sine, Cosine and Tan
     • sin(α + β) = sin(α)cos(β) + cos(α)sin(β) sin(α – β) = sin(α)cos(β) – cos(α)sin(β) cos(α + β) = cos(α)cos(β) – sin(α)sin(β) cos(α – β) = cos(α)cos(β) + sin(α)sin(β) tan(a + b) = [tan(a) + tan(b)] / [1 - tan(a)tan(b)] tan(a - b) = [tan(a) - tan(b)] / [1 + tan(a)tan(b)]

3. Double and half angle Identities

   • Double-angle formulas and Half-angle formulas
     • sin(2x) = 2sin(x)cos(x) cos(2x) = cos2(x) – sin2(x) = 1 – 2sin2(x) = 2cos2(x) – 1 tan(2x) = [2 tan(x)] / [1 - tan^2(x)]
     • sin(x/2) = +/- sqrt[(1 - cos(x))/2], cos(x/2) = +/- sqrt[(1 + cos(x))/2], tan(x/2) = +/- sqrt[(1 - cos(x))/(1 + cos(x))]