Identities:

A trigonometric equation is an identity if it is true for all the values of angle or angles involved. A given identity can be established by reducing either side to other one, or reducing each side to same expression, or any convenient modification from these.

For any of the angles A, B, C

• sin (A + B +C) = sinA cosB cosC + cosA sinB cosC + cosA cosB sinC - sinA sinB sinC
• cos (A + B +C) = cosA cosB cosC- cosA sinB sinC - sinA cosB sinC - sinA sinB cosC
•  ;
• 

If A, B, C are angles of the triangle (or A + B + C = Π):

• sinA cosB cosC + cosA sinB cosC + cosA cosB sinC = sinA sinB sinC
• cosA sinB sinC + sinA cosB sinC + sinA sinB cosC = 1 + cosA cosB cosC
• tanA + tanB + tanC = tanA tanB tanC
• cotB cotC + cotC cotA + cotA cotB = 1
• 
• 
• sin2A + sin2B + sin2C = 4sinA sinB sinC
• cos2A + cos2B + cos2C = -1-4cosA cosB cosC
• cos²A + cos²B + cos²C = 1 - 2cosA cosB cosC
• 
• 

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