sin(x+y)=sinx cosy + cosx siny

cos(x+y)=cosx cosy - sinx siny

tg(x+y)=(tgx + tgy)/(1 - tgx tgy)

ctg(x+y)=(ctgx ctgy-1)/(ctgx+ctgy)

sin(x-y)=sinx cosy - cosx siny

cos(x-y)=cosx cosy + sinx siny

tg(x-y)=(tgx - tgy)/(1 + tgx tgy)

ctg(x-y)=(ctgx ctgy + 1)/(ctgy-ctgx)

sin2x=2sinxcosx

cos2x=cos²x-sin²x=1-2sin²x=2cos²x-1

tg2x=2tgx/(1-tg²x)

ctgx2x=(ctg²x-1)/2ctgx

sinx/2=√(1-cosx)/2

cosx/2=√(1+cosx)/2

tgx/2=√(1-cosx)/(1+cosx)

ctgx/2=√(1+cosx)/(1-cosx)

sinu+sinv=2sin(u+v)/2*cos(u-v)/2

sinu-sinv=2cos(u+v)/2*sin(u-v)/2

cosu+cosv=2cos(u+v)/2*cos(u-v)/2

cosu-cosv=-2sin(u+v)/2*sin(u-v)/2

tgx+tgy=[sin(x+y)]/(cosxcosy)

ctgx+ctgy=[sin(x+y)]/(sinxsiny)

tgx-tgy=[sin(x-y)]/(cosxcosy)

ctgx-ctgy=[sin(y-x)]/(sinxsiny)