Trigonometry inverse function:-
These are most important formulae which will be very helpful in solving your questions:
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| Inverse function formulae trigonometry |
Inverse function formulae:-
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1. sin-1 (sinx) = x
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2. cos-1 (cosx) = x
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3. tan-1 (tanx) = x
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4. cot-1 (cotx) = x
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5. sec-1 (secx) = x
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6. cosec-1 (cosec) = x
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7.sin (sin-1x) = x
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8. cos (cos-1x) = x
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9. tan (tan-1x) = x
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10. cot (cot-1x) = x
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11. sec (sec-1x) = x
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12. cosec (cosec-1x) = x
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13. sin-1x = cosec-1(1/x)
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14. cos-1x = sec-1(1/x)
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15. tan-1x = cot-1(1/x)
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16. sec-1x = cos-1(1/x)
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17. cot-1x = tan-1(1/x)
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18. cosec-1x = sin-1(1/x)
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19. sin-1x + cos-1x = π/2
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20. tan-1x + cot-1x = π/2
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21. sec-1x + cosec-1x = π/2
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22. tan-1x + tan-1y = tan-1[x + y/1-xy]
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23. tan-1x – tan-1y = tan-1 [x – y/1 + xy]
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24. cot-1x + cot-1 y = cot-1 [xy-1/y + x]
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25. cot-1x – cot-1y = cot-1 [xy + 1/y – x]
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26. tan-1x + tan-1y + tan-1z = tan-1 [x + y + z – xyz/1 – xy – yz – xz]
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27. tan-1x – tan-1y + tan-1z = tan-1 [x – y + z + xyz/1 + xy + yz – xz]
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28. 2cos-1x = cos-1 (2x2 – 1)
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29. 2tan-1x = tan-1 (2x/1-x2)
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30. 2tan-1x = sin-1 (2x/1 + x2)
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31. 2tan-1x = cos-1 (1 – x2/1 + x2)
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32. 2cot-1x = cot-1 (x2 – 1/2x)
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33. 3sin-1x = sin-1 (3x – 4x3)
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34. 3cos-1x = cos-1 (4x3 – 3x)
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35. 3tan-1x = tan-1 (3x – x3/1-3x2)
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36. Sin-1(-x) = -sin-1x
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37. Cos-1(-x) = π – cos-1x
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38. tan-1(-x) = -tan-1x
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39. cot-1(-x) = π – cot-1x
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40. sec-1(-x) = π – sec-1x
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41. cosec-1(-x) = -cosec-1x
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