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Method and examples
Trigonometry
Method  

1. Simplifying trigonometric equations, proving identities
Expression
 
 
  1. `sin^2(30)*cos^2(60)`
  2. `sin(30)*cos(60)+sin(30)*cos(60)`
  3. `sin(30)*csc(30)-sin(60)*csc(60)`
  4. `2sin^2(30)*3cos^2(60)`
  5. `(2tan(60))/(1+tan^2(60))`
  6. `(3sec(60)+2tan(45)+csc(30))/(sin^2(60)+cot^2(45))`
  7. `(3sec(60)+2tan(45)+csc(30))(sin^2(60)+cot^2(45))`
  8. `sin(30)*cos(45)*tan(60)=sin(45)*cos(60)*cot(30)`
  9. `tan(45)*sec(72)*sin(58)=cos(32)*csc(18)`
  10. `sin^2(34)-cot^2(46)-cos^2(56)+tan^2(44)=sec^2(62)-csc^2(28)`
  11. `sin(30)*cos(45)*tan(60)=sin(45)*cos(60)*cot(30)`
  12. `tan(45)*sec(72)*sin(58)=cos(32)*csc(18)`
  13. `sin^2(34)-cot^2(46)-cos^2(56)+tan^2(44)=sec^2(62)-csc^2(28)`
  14. `sin^2(50)+sin^2(40)=1`
  15. `sin(35)*sec(55)-cos(55)*csc(35)=tan(25)-cot(65)`
  16. `2sin(30)+2tan(45)-3cos(60)-2cos^2(30)=0`
  17. `2sec^2(x)-2`
  18. `sin(x)sec(x)`
  19. `sin(x)cot(x)`
  20. `cot(x)sin(x)`
  21. `tan(x)+cot(x)`
  22. `cos(x)+cot(x)`
  23. `tan(x)sin(x)+cos(x)`
  24. `cot^4(x)+cot^2(x)`
  25. `cos^2(x)csc^2(x)-cos^2(x)`
  26. `tan^2(x)-sin^2(x)`
  27. `(csc(x)-sin(x))(sec(x)-cos(x))`
  28. `(tan(x)+cot(x))(sec(x)-cos(x))(csc(x)-sin(x))`
  29. `1+1/tan^2(x)`
  30. `csc(x)/cos(x)-cos(x)/sin(x)`
  31. `sec(x)/2(tan(x)+cot(x))`
  32. `sec(x)/(2(tan(x)+cot(x)))`
  33. `(tan^2(x)-cot^2(x))/(sin^2(x)-cos^2(x))`
  34. `(tan^2(x)+cot^2(x))/(tan^2(x)-cot^2(x))`
  35. `(tan^2(x)-cot^2(x))/(tan^2(x)+cot^2(x))`
  36. `(3sin(x)+5cos(x))^2+(3cos(x)-5sin(x))^2`
  37. `(1+cos(x))/sin(x)+sin(x)/(1+cos(x))`
  38. `sin^2(x)cos(x)+sin^3(x)+cos^2(x)sin(x)+cos^3(x)`
  39. `(sin^4(x)-cos^4(x))/(sin^2(x)-cos^2(x))`
  40. `5cos^2(x)+2sin^2(x)`
  41. `2cos^2(x)+sin^2(x)`
  42. `(sin^4(x)+cos^4(x))`

2. Find the value of all the other five trigonometric functions or solve expression
If = then
 
1. Find the value of all the other five trigonometric functions

 
2. Solve expression
  1. If `sin(x)=5/13` then find other trigonometry
  2. If `cos(x)=12/13` then find other trigonometry
  3. If `tan(x)=5/12` then find other trigonometry
  4. If `csc(x)=13/5` then find other trigonometry
  5. If `sec(x)=13/12` then find other trigonometry
  6. If `cot(x)=12/5` then find other trigonometry
  1. If `sin(x)=3/5` then solve `cos(x)csc(x)+tan(x)sec(x)`
  2. If `tan(x)=1/2` then solve `(1-tan^2(x))/(1+tan^2(x))+(2tan(x))/(1+tan^2(x))`
  3. If `sin(x)=4/5` then solve `(1-sin(x))/cos(x)+cos(x)/(1-sin(x))`
  4. If `cos(x)=3/5` then solve `(1-sin(x))/cos(x)+cos(x)/(1-sin(x))`

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