Triangle Identities

Trigonometric functions
sinB= b a = opposite sidehypotenuse	cosB= c a = adjacent sidehypotenuse
tanB= b c = opposite side adjacent side = sinB cosB	cotB= c b = adjacent sideopposite side = cosB sinB

Angle-Sum and -Difference Identities

sin(A+B)=sinA ‧ cosB + cosA ‧ sinB

sin(A-B)=sinA ‧ cosB- cosA ‧sinB

cos(A+B)=συνA ‧ cosB - sinA ‧ sinB

cos(A-B)=συνA ‧ cosB + sinA ‧ sinB

tan(A+B)=

tanA + tanB 1 - tanA‧tanB

tan(A-B)=

tanA - tanB 1-tanA‧tanB

cot(A+B)=

tanA‧tanB-1 tanB + tanA

cot(A-B)=

cotA‧cotB+1cotB - cotA

Double-Angle Identities

sin2A = 2sinA συνA

cos2A = συν²A - ημ²A =2συν²A-1=1-2ημ²A

tan2A =

2tanA1-tan²A

sin²A =

1-cos2A2

cos²A =

1+cos2A2

tan²A=

1-cos2A1+cos2A

Law of Sines

asinA

bsinB

csinC

Law of Cosines

a²=b²+c² - 2‧b‧c‧cosA
b²=c²+a² - 2‧c‧a‧cosB
c²=a²+b² - 2‧a‧b‧cosC

Trigonometric equations

sinx=siny ⇔ {

x=2kπ+yorx=2kπ+(π-y), κ ∈ Ζ

cosx=cosy ⇔ {

x=2kπ+yorx=2kπ-y , κ ∈ Ζ

tanX=tanY ⇔ x=kπ+y, κ ∈ Ζ

cotX=cotY ⇔x=kπ+y, κ ∈ Ζ