www.matebrunca.com Prof. Waldo Marquez Gonzalez

Ejercicios de Identidades Trigonometricas

1. csc θ · tan θ = sec θ

2. cos θ · csc θ = cot θ

3. sen2 θ + cos2 θ + tan2 θ = sec2 θ

4. sen2 Asec2 A−1

= cos2 θ

5. sec2 X1+cot2 X

= tan2 X

6. 1+tan2 θcsc2 θ

= tan2 θ

7. (sec X + tan X)(1 − sen X) = cos2 X

8. sec θ − sec θ · sen2 θ = cos θ

9. sen X · sec X · cot X = 1

10. cos θ · sec θ = 1

11. sen2 β(1 + cot2 β) = 1

12. sen2 θ · sec2 θ − sec2 θ = −1

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www.matebrunca.com Prof. Waldo Marquez Gonzalez

13. (sen α + cos α)2 + (sen α− cos α)2 = 2

14. tan2 θ · cos2 θ + cot2 θ · sen2 θ = 1

15. tan θ + cos θ1+sen θ = sec θ

16. sen X+cos Xsen X = 1 − 1

tan X

17. cos θcot θ = sen θ

18. sen αcsc α + cos α

sec α = 1

19. tan βsen β = sec β

20. sec θtan θ+cot θ = sen θ

21. csc θcot θ = sec θ

22. 1−sen θcos θ = cos θ

1+sen θ

23. sen4 θ = 1−cos2 θcsc2 θ

24. sec θ(1 − sen2 θ) = cos θ

25. tan θ · cos θ · csc θ = 1

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www.matebrunca.com Prof. Waldo Marquez Gonzalez

26. sen κ · sec κ = tan κ

27. 1sec θ+tan θ = sec θ − tan θ

28. tan θ + cot θ = 1sen θ·cos θ

29. csc θtan θ+cot θ = cos θ

30. sen θcot θ = sec θ − cos θ

31. cos2 β = (1 + sen β)(1 − sen β)

32. 1−sen α(sec α−tan α)2

= 1 + sen α

33. (1 − sen2 γ)(1 + tan2 γ) = 1

34. tan δ + cot δ = sec δ · csc δ

35. (tan ψ + cot ψ) tan ψ = sec2 ψ

36. tan2 µ · cot2 µ = sen2 µ + cos2 µ

37. tan σ−sen σsen3 σ

= sec σ1+cos σ

38. 11+sen ρ + 1

1−sen ρ = 2 sec2 ρ

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www.matebrunca.com Prof. Waldo Marquez Gonzalez

39. tan2 φ · csc2 φ · cot2 φ · sen2 φ = 1

40. cot2 φ(1 + tan2 φ) = csc2 φ

41. sen φ+cos φcos φ = 1 + tan φ

42. cos µ(tan µ + cot µ) = csc µ

43. sec2 κ−1sec2 κ

= sen κ

44. 1+tan2 ψtan2 ψ

= csc2 ψ

45. cot θ−11−tan θ = cot θ

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Bibliograf ıa

[1] Baldor, Aurelio. Geometrıa Plana y del Espacio y Trigonometrıa.

[2] Meneses, Roxanna. Matematica:ensenanza-aprendizaje. UndecimoAno.

[3] Swokowski, Earl. Algebra y Trigonometrıa con Geometrıa Analıtica.

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