Inverse trigonometric function formula

Trigonometry inverse function:-

These are most important formulae which will be very helpful in solving your questions:

Inverse function formula, trigonometry formula
Inverse function formulae trigonometry

Inverse function formulae:-


1. sin-1 (sinx) = x
2. cos-1 (cosx) = x
3. tan-1 (tanx) = x
4. cot-1 (cotx) = x
5. sec-1 (secx) = x
6. cosec-1 (cosec) = x
7.sin (sin-1x) = x
8. cos (cos-1x) = x
9. tan (tan-1x) = x
10. cot (cot-1x) = x
11. sec (sec-1x) = x
12. cosec (cosec-1x) = x
13. sin-1x = cosec-1(1/x)
14. cos-1x = sec-1(1/x)
15. tan-1x = cot-1(1/x)
16. sec-1x = cos-1(1/x)
17. cot-1x = tan-1(1/x)
18. cosec-1x = sin-1(1/x)
19. sin-1x + cos-1x = π/2
20. tan-1x + cot-1x = π/2
21. sec-1x + cosec-1x = π/2
22. tan-1x + tan-1y = tan-1[x + y/1-xy]
23. tan-1x – tan-1y = tan-1 [x – y/1 + xy]
24. cot-1x + cot-1 y = cot-1 [xy-1/y + x]
25. cot-1x – cot-1y = cot-1 [xy + 1/y – x]
26. tan-1x + tan-1y + tan-1z = tan-1 [x + y + z – xyz/1 – xy – yz – xz]
27. tan-1x – tan-1y + tan-1z = tan-1 [x – y + z + xyz/1 + xy + yz – xz]
28. 2cos-1x = cos-1 (2x2 – 1)
29. 2tan-1x = tan-1 (2x/1-x2)
30. 2tan-1x = sin-1 (2x/1 + x2)
31. 2tan-1x = cos-1 (1 – x2/1 + x2)
32. 2cot-1x = cot-1 (x2 – 1/2x)
33. 3sin-1x = sin-1 (3x – 4x3)
34. 3cos-1x = cos-1 (4x3 – 3x)
35. 3tan-1x = tan-1 (3x – x3/1-3x2)
36. Sin-1(-x) = -sin-1x
37. Cos-1(-x) = π – cos-1x
38. tan-1(-x) = -tan-1x
39. cot-1(-x) = π – cot-1x
40. sec-1(-x) = π – sec-1x
41. cosec-1(-x) = -cosec-1x

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