Vivax Solutions

1. cos⁴A - sin⁴A + 1 ≡ 2 cos²A
2. (sinA+cosA)(1-sin A cos A)≡ sin³A + cos³A
3. sin A / (1 + cos A) + (1 + cos A) /sin A ≡ 2 cosec A
4. cos⁶A + sin⁶A ≡ 1-3 sin²A cos²A
5. cosec A / (cosecA - 1) + cosec A/(cosecA + 1) ≡ 2 sec²A
6. cosec A/(cot A + tan A) ≡ cos A
7. (sec A + cos A) (sec A - cos A) ≡ tan²A + sin²A
8. 1 / (cot A + tan A) ≡ sin A cos A
9. 1 / (sec A - tan A) ≡ sec A + tan A
10. (1 - tan A) / (1 + tan A) ≡ (cot A -1) / (cot A + 1)
11. (1 + tan²A) / (1 + cot²A) ≡ sin²A / cos²A
12. (sec A-tan A) / (sec A + tan A) ≡ 1-2 sec A tan A + 2 tan²A
13. tan A / (1 - cot A) + cot A / (1 - tan A) ≡ sec A cosec A + 1
14. cos A / (1 - tan A) + sin A / (1-cot A) ≡ sin A + cos A
15. (sin A + cos A)(cot A + tan A) ≡ sec A + cosec A
16. sec⁴A - sec²A ≡ tan⁴A + tan²A
17. cot⁴A + cot²A ≡ cosec⁴A - cosec² A
18. sec²A cosec²A ≡tan²A + cot²A + 2
19. tan²A - sin²A ≡ sin⁴A sec²A
20. (1 + cot A - cosec A) (1 + tan A + sec A) ≡ 2
21. 1/(cosec A - cot A) - 1/(sin A) ≡ 1/sin A - 1/(cosec A + cot A)
22. cot A cos A/(cot A + cos A) ≡ (cot A - cos A)/(cot A cos A)
23. cot A + tan B/(cot B + tan A) ≡ cot A tan B
24. 1/(sec²a-cos²a) + 1/(cosec²a-sin²a) cos²a sin²a ≡ 1-(cos²a sin²a) / (2 + cos²a sin²a)
25. sin⁸A - cos⁸ A ≡ (sin²A - cos²A) (1-2 sin²A cos²A)
26. (cos A cosec A - sin A sec A) / (cos A + sin A) ≡ cosec A - sec A
27. (tan A + sec A - 1) / (tan A - sec A + 1) ≡ (1 + sin A) / cos A
28. (tan α + cosec β)² - (cot β - sec α)² ≡ 2tan αcot β(cosec α + sec β)
29. 2 sec²a - sec⁴ a - 2 cosec²a ≡ cot⁴a - tan⁴a
30. (sin a + cosec a)² + (cos a + sec a)² ≡ tan²a + cot²a + 7
31. (1+cot A + tan A) (sin A - cos A) ≡ sec A / cosec²A - cosec A / sec²A
32. sin 2A / (1 + cos 2A) ≡ tan A
33. sin 2A / (1 - cos 2A) = cot A
34. (1 - cos 2A) / (1 + cos 2A) ≡ tan² 35. tan A + cot A ≡ 2 cosec 2A
36. tan A - cot A = -2 cot 2A
37. cosec 2A + cot 2A ≡ cot A
38. [1 - cos A + cos B - cos (A+B)] / [1 + cos A - cos B - cos (A+B)] ≡ tan (A/2) cot (B/2)
39. cos A / (1 + sin A) ≡ tan (45 - A/2)
40. (sec8A - 1) / (sec 4A - 1) = tan 8A / tan 2A
41. [1 + tan²2 42. (sin a + sin b) / (sin a - sin b) ≡ tan (a + b) /2 / tan (a- b) / 2
43. (sin²²B) / sin A cos A - sin B cos B ≡ tan (A+B)
44. (cos A + sin A) / (cos A - sin A) - (cos A - sin A) / (cos A + sin A) ≡2 tan 2A
45. cot(A + 15) - tan (A - 15 ) ≡ 4 cos 2A / (1 + 2 sin 2A)
46. sin x + sin 2x / (1 + cos x + cos 2x) ≡ tan x
47. (1 + sin x - cos x) / (1 + sin x + cos x) ≡ tan x/2
48. sin(A + 3B) + sin(3A+B) / sin 2A + sin 2B ≡ 2 cos(A+B)
49. sin 3A + sin 2A - sin A ≡ 4 sin A cos A/2 cos 3A/2
50.tan 2A ≡ (sec 2A + 1) (sec 2A - 1).