Trig Identities
tan(x/2)= ±√((1-cosx)/(1+cosx))=sinx/(1+cosx)
(1-cosx)/sinx
cos²x (half-angle)=
(1/2)[1+cos(2x)]
sin²x (half-angle)=
(1/2)[1-cos(2x)]
cosxcosy=
(1/2)[cos(x-y)+cos(x+y)]
sinxsiny=
(1/2)[cos(x-y)+cos(x+y)]
sinxcosy=
(1/2)[sin(x+y)+sin(x-y)]
cosxsiny=
(1/2)[sin(x+y)-sin(x-y)]
tan(x+y)=
(tanx+tany)/(1-tanxtany)
tan(x-y)=
(tanx-tany)/(1+tanxtany)
cosx-cosy=
-2sin[(x+y)/2]sin[(x-y)/2]
sin(-x)=
-sin(x)
cos(x+π/2)=
-sinx
tan(-x)=
-tan(x)
cos(2x)=cos²x-sin²x=2cos²x-1
1-2sin²x
secx=
1/cosx
cscx=
1/sinx
cotx= cosx/sinx=
1/tanx
cosx+cosy=
2cos[(x+y)/2]cos[(x-y)/2]
cos(2x)=cos²x-sin²x=1-2sin²x=
2cos²x-1
sinx+siny=
2sin[(x+y)/2]cos[(x-y)/2]
sinx-siny=
2sin[(x-y)/2]cos[(x+y)/2]
sin(2x)=
2sinxcosx
tan(2x)=
2tanx/(1-tan²x)
tan²x (half-angle)=
[1-cos(2x)]/[1+cos(2x)]
cos(-x)=
cos(x)
sin(x+π/2)=
cosx
cotx= 1/tanx=
cosx/sinx
cos(x-y)=
cosxcosy+sinxsiny
cos(x+y)=
cosxcosy-sinxsiny
cos(2x)=1-2sin²x=2cos²x-1
cos²x-sin²x
Pythagorean Identity 3
cot²x+1=csc²x
tan(x/2)= ±√((1-cosx)/(1+cosx))=(1-cosx)/sinx=
sinx/(1+cosx)
tanx=
sinx/cosx
sin(x+y)=
sinxcosy+cosxsiny
sin(x-y)=
sinxcosy-cosxsiny
Pythagorean Identity 1
sin²x+cos²x=1
Pythagorean Identity 2
tan²x+1=sec²x
cos(x/2)=
±√((1+cosx)/2))
tan(x/2)=(1-cosx)/sinx=sinx/(1+cosx)
±√((1-cosx)/(1+cosx))
sin(x/2)=
±√((1-cosx)/2))