Relations between Inverse Trigonometric Functions

Posted In: Mathematics
  1. $sin^{-1}(-x)=-sin^{-1}x$
  2. $sin^{-1}x=π/2-cos^{-1}x$
  3. $sin^{-1}x=cos^{-1}√{1-x^2}, 0≤x≤1$
  4. $sin^{-1}x=-cos^{-1}√{1-x^2}, -1≤x≤0$
  5. $sin^{-1}x=tan^{-1}x/√{1-x^2}, x^2<1$
  6. $sin^{-1}x=cot^{-1}√{1-x^2}/x, 0< x≤1$
  7. $sin^{-1}x=cot^{-1}√{1-x^2}/x-π, -1≤x<0$
  8. $cos^{-1}(-x)=π-cos^{-1}x$
  9. $cos^{-1}x=π/2-sin^{-1}x$
  10. $cos^{-1}x=sin^{-1}√{1-x^2}, 0≤x≤1$
  11. $cos^{-1}x=π-sin^{-1}√{1-x^2},-1≤x≤0$
  12. $cos^{-1}x=tan^{-1}√{1-x^2}/x,0< x≤1$
  13. $cos^{-1}x=π+tan^{-1}√{1-x^2}/x,-1≤x<0$
  14. $cos^{-1}x=cot^{-1}x/√{1-x^2},-1≤x≤1$
  15. $tan^{-1}(-x)=tan^{-1}x$
  16. $tan^{-1}x=π/2-cot^{-1}x$
  17. $tan^{-1}x=sin^{-1}{x/√{1+x^2}}$
  18. $tan^{-1}x=cos^{-1}{1/√{1+x^2}}x,x≥0$
  19. $tan^{-1}x=-cos^{-1}{1/√{1+x^2}}x,x≤0$
  20. $tan^{-1}x=π/2-tan^{-1}1/x,x>0$
  21. $tan^{-1}x=-π/2-tan^{-1}1/x,x<0$
  22. $tan^{-1}x=cot^{-1}1/x,x>0$
  23. $tan^{-1}x=cot^{-1}1/x-π,x<0$
  24. $cot^{-1}(-x)=π-cot^{-1}x$
  25. $cot^{-1}x=π/2-tan^{-1}x$
  26. $cot^{-1}x=sin^{-1}{1/√{1+x^2}},x>0$
  27. $cot^{-1}x=π-sin^{-1}{1/√{1+x^2}},x<0$
  28. $cot^{-1}x=cos^{-1}{x/√{1+x^2}}$
  29. $cot^{-1}x=tan^{-1}1/x, x>0$
  30. $cot^{-1}x=π+tan^{-1}1/x, x<0$

Post Tags: Trigonometry


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