Double angle formula and deformation formula tan2a = 2tana/(1-tan2a) cot2a = (cot2a-1)/2cota.
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
sinα+sin(α+2π/n)+sin(α+2π* 2/n)+sin(α+2π* 3/n)+……+sin[α+2π*(n- 1)/n]= 0
cosα+cos(α+2π/n)+cos(α+2π* 2/n)+cos(α+2π* 3/n)+……+cos[α+2π*(n- 1)/n]= 0
sin^2(α)+sin^2(α-2π/3)+sin^2(α+2π/3)=3/2
tanAtanBtan(A+B)+tanA+tan B- tan(A+B)= 0
Sum of product sinαsinβ =[cos(α-β)-cos(α+β)]/2.
cosαcosβ=[cos(α+β)+cos(α-β)]/2
sinαcosβ=[sin(α+β)+sin(α-β)]/2
cosαsinβ=[sin(α+β)-sin(α-β)]/2
Half-angle formula tan (a/2) = (1-COSA)/Sina = Sina/(1+COSA)
cot(A/2)= sinA/( 1-cosA)=( 1+cosA)/sinA
sin^2(a/2)=( 1-cos(a))/2
cos^2(a/2)=( 1+cos(a))/2
tan(a/2)=( 1-cos(a))/sin(a)= sin(a)/( 1+cos(a))
Trigonometric function defines that trigonometric function is a function of angle; They are very important in studying triangles, simulating periodic phenomena and many other applications. Trigonometric function is usually defined as the ratio of two sides of a right triangle containing this angle, and it can also be equivalently defined as the lengths of various line segments on the unit circle. More modern definitions express them as infinite series or solutions of specific differential equations, allowing them to be extended to any positive and negative values, even complex values.