1. sec θ - tan θ sin θ = cos θ
2. cot²α(1 - cos²α) = cos²α
3. (1 + sec β) / (sin β + tan β) = csc β
4. (1 + sin φ) / cos φ = cos φ / (1 - sin φ)
5. sin²t - cos²t = 1 - 2cos²t
6. tan γ / (sec γ - 1) = sec γ + 1 / tan γ
7. (sin θ - sin θ cos θ) / (sin θ + sin θ tan θ) = (1 - cos θ) / (1 + tan θ)
8. cos²α / (1 - sin α) = 1 + sin α
9. sec²t csc²t = sec²t + csc²t
10. (sec x - csc x) / (sec x + csc x) = (tan x - 1) / (tan x + 1)
11. 1 - cos²β / (1 + sin β) = sin β
12. (sin φ + tan φ) / (cot φ + csc φ) = sin φ tan φ
13. (sin α cos α) / (csc²α - sin²α) = tan α / (1 - tan²α)
14. (sin θ - cos θ) / cos θ + 1 = tan θ
15. 1 / (tan θ + tan θ) = sec θ csc θ
16. (1 + cos ω) / (1 - cos ω) = (sec ω + 1) / (sec ω - 1)
17. (sin ω + tan ω) / sin ω = 1 + sec ω
18. (sec β + csc β) / (1 + tan β) = csc β
19. (1 - sin θ)(sec θ + tan θ) = cos θ
20. (sec γ - tan γ)² = (1 - sin γ) / (1 + sin γ)
21. sin²t - cos²t = 2sin²t - 1
22. (cot θ + tan θ) / (sin θ cos θ) = csc²θ sec²θ
23. csc α / (1 - cos²α) = sec α tan α
24. tan φ / (1 + tan²φ) = sin φ cos φ
25. tan²θ / sec θ = sec θ - cos θ
26. cos t csc t + tan t = csc t sec t
27. cos α / (1 + sin α) + (1 + sin α) / cos α = 2 sec α
28. (tan θ - cot θ) / (tan θ + cot θ) = (tan²θ - 1) / (sec²θ)
29. cot β / (1 + cot²β) = sin β cos β
30. (tan φ + 1) / (sin φ + cos φ) = sec φ
31. cos²ψ - sin²ψ = (1 - tan²ψ) / (1 + tan²ψ)
32. sin μ / (1 + cos μ) = csc μ - cot μ
33. cot²θ - csc²θ = -csc²θ cot²θ
34. cos⁴φ - sin⁴φ = cos²φ - sin²φ
35. sin³α + cos³α = (sin α + cos α)(1 - sin α cos α)
36. (tan φ + cot φ)² = sec²φ + csc²φ
37. (sin β + cos β)(sec β + csc β) = tan β + cot β
38. sin φ / (1 - cos φ) - cot φ = csc φ
39. (tan μ sin μ) / (tan μ + sin μ) = (tan μ - sin μ) / (tan μ sin μ)
40. (sec θ + csc θ) / (tan θ + cot θ) = sin θ + cos θ
41. csc²t - sec²t = cot²t - tan²t
42. (sin³α + csc³α) / (sin α + csc α) = csc²α - cos²α
43. (cos φ sin²φ) / (1 + cos φ) = cos φ - cos²φ
44. sin β / (1 + cos β) + (1 + cos β) / sin β = 2 cot β sec β
45. sec θ / (cot θ + tan θ) = sin θ
46. sin²t + sin²t tan²t = tan²t
Parent Tip: Review the logic above to help your child master the concept of proving trigonometric identities worksheet.
