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Trigonometric Id.

Formula

Theorems/PropertiesFormulas/Definitions
Even/Odd Identities. cos (-u) = cos(u) and sec(-u) = sec(u). the remaining 4 are odd functions.
Sum and difference identities for cosine. cos(a+b) = cos(a)cos(b) - sin(a)sin(b). cos(a-b) = cos(a)cos(b) + sin(a)sin(b).
Sum and difference identities for sine. sin(a+b) = sin(a)cos(b) + cos(a)sin(b). sin(a-b) = sin(a)cos(b) - cos(a)sin(b).
Cofunction identities. cos(pi/2 - u) = sin(u) and sin(pi/2 - u) = cos(u). sec(pi/2 - u) = csc(u) and csc(pi/2 - u) = sec(u). tan(pi/2 - u) = cot(u) and cot(pi/2 - u) = tan(u).
Double angle identity. cos(2x) = cos² - sin²(x). sin(2x) = 2*sin(x)cos(x). tan(2x) = (2*tan(x))/(1 - tan²(x)).
Power reduction formulas. cos²(x) = (1/2)*(1 + cos(2x)). sin²(x) = (1/2)*(1 - cos(2x)).
Half angle formulas. cos(x/2) = -/+ sqrt[(1/2)*(1 + cos(x))]. sin(x/2) = -/+ sqrt[(1/2)*(1 - cos(x))]. tan(x/2) = -/+ sqrt[(1 - cos(x))/(1 + cos(x))].
Sum to product formulas. cos(a) + cos(b) = 2*cos[(1/2)*(a + b)]*cos[(1/2)*(a - b)]. cos(a) - cos(b) = -2*sin[(1/2)*(a + b)]*sin[(1/2)*(a - b)]. sin(a) +/- sin(b) = 2*sin[(1/2)*(a +/- b)]*cos[(1/2)*(a -/+ b)].
Product to sum formulas. cos(a)cos(b) = (1/2)*[cos(a - b) + cos( a + b)]. sin(a)sin(b) = (1/2)*[cos(a - b) - cos(a + b)]. sin(a)cos(b) = (1/2)*[sin(a - b) + sin(a + b)].
Created by: JuniorDBlackbone