Trigonometric function and its transformation

Reciprocal	Sin α * CSC α = 1	Cos α * sec α = 1	Tan α * cot α = 1
Commodity count	Tan α = sin α/COS α	Cot α = cos α/sin α
Sum of squares	Sin2 α + cos2 α = 1	1 + tan2 α = sec2 α	1 + cot2 α = csc2α
Two corners and	Sin (α ± β) = sin α cos β + cos α sin β	Cos (α ± β) = cos α cos β-+ sin α sin β	Tan (α ± β) = (TAN α ± tan β)/(1-+ Tan α tan β)
Times Angle	Sin2 α = 2sin α cos α	Cos2 α = cos2 α-sin2 α = 2cos2 α-1 = 1-2sin2 α	Tan2 α = 2tan α/(1-tan2 α)
Halfwidth	Sin (α/2) = [(1-Cos α)/2] ^ 0.5	Cos (α/2) = [(1 + cos α)/2] ^ 0.5	Tan (α/2) = [(1-Cos α)/(1 + cos α)] ^ 0.5
Sum Product	Sin α cos β = [Sin (α + β) + sin (α-β)]/2	Cos α sin β = [Sin (α + β)-sin (α-β)]/2
Sum Product	Sin α sin β = [Cos (α + β) + cos (α-β)]/2	Cos α cos β =-[Cos (α + β)-cos (α-β)]/2
Product Sum	Sin α + sin β = 2sin [(α + β)/2] cos [(α-β)/2]	Sin α-Sin β = 2cos [(α + β)/2] sin [(α-β)/2]
Product Sum	Cos α + cos β = 2cos [(α + β)/2] cos [(α-β)/2]	Cos α-Cos β =-2sin [(α + β)/2] sin [(α-β)/2]