Trigonometric Identities

Trigonometric Identities

1. For Sine

   • sin(α+β)=sinαcosβ+sinβcosα
   • sin(α-β)=sinαcosβ-sinβcosα

2. For Cosine

   • cos(α+β)=cosαcosβ-sinαsinβ
   • cos(α-β)=cosαcosβ+sinαsinβ

3. For Tangent

   • tan(α+β)=(tanα+tanβ)/(1-tanαtanβ)
   • tan(α-β)=(tanα-tanβ)/(1+tanαtanβ)

4. Double angle

   • sin(2x)=2sinxcosx
   • cos(2x)=(cos)^2 x-(sin)^2 x = 1-2(sin)^2 x = 2(cos)^2 x-1
   • tan(2x)=2tanx/(1-(tan)^2 x)

5. Half-angle

   • sin (x/2): √(1-cosx)/2
   • cos(x/2): √(1+cosx)/2
   • tan (x/2): (1-cosx)/sinx=sinx/(1+cosx)