推選答案sin²a+cos²a=1
1+tan²a=sec²a
1+cot²a=csc²a
sina/cosa=tana
seca/csca=tana
cosa/sina=cota
sin2α = 2cosαsinα
= sin²(α+π/4)-cos²(α+π/4)
= 2sin²(a+π/4)-1
= 1-2cos²(α+π/4)
cos2α = cos²α-sin²α
= 1-2sin²α
= 2cos²α-1
= 2sin(α+π/4)·cos(α+π/4)
tan2α = 2tanα/[1-(tanα)²]
sin3α = 3sinα-4sin³α
cos3α = 4cos³α-3cosα
tan3α = (3tanα-tan³α)/(1-3tan²α)
sin3α = 4sinα·sin(π/3-α)·sin(π/3+α)
cos3α = 4cosα·cos(π/3-α)·cos(π/3+α)
tan3α = tanα·tan(π/3-α)·tan(π/3+α)
sin(nα) = ncos(n-1)α·sinα - C(n,3)cos(n-3)α·sin3α + C(n,5)cos(n-5)α·sin5α-…
cos(nα) = cosnα - C(n,2)cos(n-2)α·sin2α + C(n,4)cos(n-4)α·sin4α

Asinα+Bcosα = √(A2+B2)sin[α+arctan(B/A)]
Asinα+Bcosα = √(A2+B2)cos[α-arctan(A/B)]
sin(α/2) = ±√[(1-cosα)/2]
cos(α/2) = ±√[(1+cosα)/2]
tan(α/2) = ±√[(1-cosα)/(1+cosα)]=sinα/(1+cosα)=(1-cosα)/sinα=cscα-cotα
cot(α/2) = ±√[(1+cosα)/(1-cosα)]=(1+cosα)/sinα=sinα/(1-cosα)=cscα+cotα
sec(α/2) = ±√[(2secα/(secα+1)]
csc(α/2) = ±√[(2secα/(secα-1)]
kπ+a
sin（2kπ+α）=sinα
cos（2kπ+α）=cosα
tan（kπ+α）=tanα
cot（kπ+α）=cotα
sec（2kπ+α）=secα
csc（2kπ+α）=cscα
sin（π+α）=－sinα
cos（π+α）=－cosα
tan（π+α）=tanα
cot（π+α）=cotα
sec(π+α)=-secα
csc(π+α)=-cscα

-a
sin（－α）=－sinα
cos（－α）=cosα
tan（－α）=－tanα
cot（－α）=－cotα
sec(-α)=secα
csc(-α)=-cscα

π-a
sin（π－α）=sinα
cos（π－α）=-cosα
tan（π－α）=－tanα

cot（π－α）=－cotα
sec(π-α)=-secα
csc(π-α)=cscα

π/2±a
sin（π/2+α）=cosα
cos（π/2+α）=－sinα
tan（π/2+α）=－cotα
cot（π/2+α）=－tanα
sec(π/2+α)=-cscα
csc(π/2+α)=secα
sin（π/2－α）=cosα
cos（π/2－α）=sinα
tan（π/2－α）=cotα
cot（π/2－α）=tanα
sec(π/2-α)=cscα
csc(π/2-α)=secα

3π/2±a
sin（3π/2+α）=－cosα
cos（3π/2+α）=sinα
tan（3π/2+α）=－cotα
cot（3π/2+α）=－tanα
sec(3π/2+α)=cscα
csc(3π/2+α)=-secα
sin（3π/2－α）=－cosα
cos（3π/2－α）=－sinα
tan（3π/2－α）=cotα
cot（3π/2－α）=tanα
sec(3π/2-α)=-cscα
csc(3π/2-α)=-secα
tan(a+π/4）=(tan a+1）/（1-tan a)
tan(a-π/4）=(tan a-1）/（1+tan a)
asinx+bcosx=[√（a²+b²）]{[a/√（a²+b²）]sinx+[b/√（a²+b²）]cosx}=[√（a²+b²）]sin(x+y)

sinα·cosβ=（1/2）[sin（α+β）+sin（α-β）]
cosα·sinβ=（1/2）[sin（α+β）-sin（α-β）]
cosα·cosβ=（1/2）[cos（α+β）+cos（α-β）]
sinα·sinβ= -（1/2）[cos（α+β）-cos（α-β）]
sinA+sinB+sinC=4cos（A/2）cos（B/2）cos（C/2）
cosA+cosB+cosC=1+4sin（A/2）sin（B/2）sin（C/2）
tanA+tanB+tanC=tanAtanBtanC
cot（A/2）+cot（B/2）+cot（C/2）=cot（A/2）cot（B/2）cot（C/2）
tan(A/2)tan(B/2)+tan(B/2)tan(C/2)+tan(C/2)tan(A/2)=1
cotAcotB+cotBcotC+cotCcotA=1
(cosA)^2+(cosB)^2+(cosC)^2+2cosAcosBcosC=1
sin2A+sin2B+sin2C=4sinAsinBsinC