• ## 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

 Trigonometric identities sin2x+cos2x=1 cos2x= 1 1+tan2x tanX= sinX cosX = 1 cotX sin2x= tan2x1+tan2x cotX= cosXsinX = 1tanX tanX‧cotX=1

 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

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