This document lists various trigonometric identities including: 1) Definitions of trig functions like sine, cosine, tangent, cotangent, secant, and cosecant 2) Identities involving negative angles 3) Sum and difference identities for trig functions of summed or subtracted angles 4) Double angle and half angle identities 5) Product-to-sum and sum-to-product identities 6) Pythagorean identities relating trig functions to their squares

1. Identidades Trigonom´tricas Fundamentales
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1 1
1. csc(x) = 2. sec(x) =
sin(x) cos(x)
sin(x) cos(x)
3. tan(x) = 4. cot(x) =
cos(x) tan(x)
5. 1 + tan2 (x) = sec2 (x) 6. 1 + cot2 (x) = csc2 (x)
7. sin(−x) = − sin(x) 8. cos(−x) = cos(x)
π
9. tan(−x) = − tan(x) 10. sin − x = cos(x)
2
π π
11. cos − x = sin(x) 12. tan − x = cot(x)
2 2
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F´rmulas de Suma y Resta de Angulos
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1. sin(x + y) = sin(x) cos(y) + cos(x) sin(y) 2. sin(x − y) = sin(x) cos(y) − cos(x) sin(y)
3. cos(x + y) = cos(x) cos(y) − sin(x) sin(y) 4. cos(x − y) = cos(x) cos(y) + sin(x) sin(y)
tan(x) + tan(y) tan(x) − tan(y)
5. tan(x + y) = 6. tan(x − y) =
1 − tan(x) tan(y) 1 + tan(x) tan(y)
Identidades de Productos
1 1
1. sin2 (x) = (1 − cos (2 x)) 2. cos2 (x) = (1 + cos (2 x))
2 2
1 1
3. sin (x) cos (x) = sin (2 x) 4. sin (x) sin (y) = (cos (x − y) − cos (x + y))
2 2
1 1
5. sin (x) cos (y) = (sin (x − y) + sin (x + y)) 6. cos (x) cos (y) = (cos (x − y) + cos (x + y))
2 2
´
F´rmulas del Doble de un Angulo
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1. sin (2 x) = 2 sin (x) cos (x) 2. cos (2 x) = cos2 (x) − sin2 (x)
2 tan (x)
3. cos (2 x) = 2 cos2 (x) − 1 4. tan (2 x) =
1 − tan2 (x)
(c) Departamento de Matem´ticas. ITESM, Campus Monterrey
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