Demostras las siguientes identidades:
1. sen x ctg x = cos x
2. cos x tg x = sen x
3. ctg x sec x = cosec x
4. sen x sec x = tg x
5. cos x cosec x = ctg x
6. ctg x sec x sen x = 1
7. (1 - cos² x) cosec² x = 1
8. (1 - sen² x) sec² x = 1
9. ctg² x (1 - cos² x) = cos² x
10. (1 - cos² x) sec² x = tg² x
11. cosec x √1 - sen² x = ctg x
12. (1 + tg² x) cos² x = 1
13. (sec² x - 1) ctg² x = 1
14. (1 - cos² x)(1 + tg² x) = tg² x
15. cos x cosec x √sec² x - 1 = 1
16. sen² x (1 + ctg² x) = 1
17. (cosec² x - 1) tg² x = 1
18. (1 - cos² x)(1 + ctg² x) = 1
19. sen x sec x √cosec² x - 1 = 1
20. cos x √ctg² x + 1 = √cosec² x - 1
21. sen² x ctg² x + sen² x = 1
22. (1 + tg² x)(1 - sen² x) = 1
23. sen² x sec² x = sec² x - 1
24. cosec² x tg² x - 1 = tg² x
1 1
25. ------- + ---------- = 1
sec² x cosec² x
1 1
26.-------- - ------- = 1
cos² x ctg² x
sen x cos x
27. -------- + ------- = 1
cosec x sec x
sec x tg x
28. ------- - ------- = 1
cos x ctg x
29. sen4 x - cos4 x = 2 sen² x - 1 = 1 - 2 cos² x
30. sec4 x - 1 = 2 tg² x + tg4 x
31. cosec4 x - 1 = 2 ctg² x + ctg4 x
32. (tg x cosec x)² - (sen x sec x)² = 1
33. (sec x ctg x)² - (cos x cosec x)² = 1
34. tg² x - ctg² x = sec² x - cosec² x
sen x ctg² x 1 sec² x ctg x
35. A. -------------- = ---- ;; B. ---------------- = tg x
cos x tg x cosec² x
36. A. sec x - tg x sen x = cos x ; B. tg x + ctg x = sec x cosec x
37. (1 + ctg² x)1/2 (sec² x - 1)1/2 (1 - sen² x)1/2 = 1
38. (cos x + sen x)² + (cos x - sen x)² = 2
39. (1 + tg x)² + (1 - tg x)² = 2 sec² x
1. sen x ctg x = cos x
2. cos x tg x = sen x
3. ctg x sec x = cosec x
4. sen x sec x = tg x
5. cos x cosec x = ctg x
6. ctg x sec x sen x = 1
7. (1 - cos² x) cosec² x = 1
8. (1 - sen² x) sec² x = 1
9. ctg² x (1 - cos² x) = cos² x
10. (1 - cos² x) sec² x = tg² x
11. cosec x √1 - sen² x = ctg x
12. (1 + tg² x) cos² x = 1
13. (sec² x - 1) ctg² x = 1
14. (1 - cos² x)(1 + tg² x) = tg² x
15. cos x cosec x √sec² x - 1 = 1
16. sen² x (1 + ctg² x) = 1
17. (cosec² x - 1) tg² x = 1
18. (1 - cos² x)(1 + ctg² x) = 1
19. sen x sec x √cosec² x - 1 = 1
20. cos x √ctg² x + 1 = √cosec² x - 1
21. sen² x ctg² x + sen² x = 1
22. (1 + tg² x)(1 - sen² x) = 1
23. sen² x sec² x = sec² x - 1
24. cosec² x tg² x - 1 = tg² x
1 1
25. ------- + ---------- = 1
sec² x cosec² x
1 1
26.-------- - ------- = 1
cos² x ctg² x
sen x cos x
27. -------- + ------- = 1
cosec x sec x
sec x tg x
28. ------- - ------- = 1
cos x ctg x
29. sen4 x - cos4 x = 2 sen² x - 1 = 1 - 2 cos² x
30. sec4 x - 1 = 2 tg² x + tg4 x
31. cosec4 x - 1 = 2 ctg² x + ctg4 x
32. (tg x cosec x)² - (sen x sec x)² = 1
33. (sec x ctg x)² - (cos x cosec x)² = 1
34. tg² x - ctg² x = sec² x - cosec² x
sen x ctg² x 1 sec² x ctg x
35. A. -------------- = ---- ;; B. ---------------- = tg x
cos x tg x cosec² x
36. A. sec x - tg x sen x = cos x ; B. tg x + ctg x = sec x cosec x
37. (1 + ctg² x)1/2 (sec² x - 1)1/2 (1 - sen² x)1/2 = 1
38. (cos x + sen x)² + (cos x - sen x)² = 2
39. (1 + tg x)² + (1 - tg x)² = 2 sec² x
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