Formulas for Sum and Difference of Inverse Trigonometric Functions

  1. Si{n^{ - 1}}a + Si{n^{ - 1}}b = Si{n^{ -       1}}(a\sqrt {1 - {b^2}} + b\sqrt {1       - {a^2}} )

  2. Si{n^{ - 1}}a - Si{n^{ - 1}}b = Si{n^{ -       1}}(a\sqrt {1 - {b^2}} - b\sqrt {1       - {a^2}} )

  3. Co{s^{ - 1}}a + Co{s^{ - 1}}b = Co{s^{ -       1}}(ab - \sqrt {(1 - {a^2})(1 - {b^2})} )

  4. Co{s^{ - 1}}a - Co{s^{ - 1}}b = Co{s^{ -       1}}(ab + \sqrt {(1 - {a^2})(1 - {b^2})} )

  5. Ta{n^{ - 1}}a + Ta{n^{ - 1}}b = Ta{n^{ -       1}}\left( {\frac{{a + b}}{{1 - ab}}} \right)

  6. Ta{n^{ - 1}}a - Ta{n^{ - 1}}b = Ta{n^{ -       1}}\left( {\frac{{a - b}}{{1 + ab}}} \right)

  7. Si{n^{ - 1}}\left( {\frac{{2a}}{{1 + {a^2}}}}       \right) = 2Ta{n^{ - 1}}a

  8. Co{s^{ - 1}}\left( {\frac{{1 - {a^2}}}{{1 +       {a^2}}}} \right) = 2Ta{n^{ - 1}}a

  9. Ta{n^{ - 1}}\left( {\frac{{2a}}{{1 - a}}}       \right) = 2Ta{n^{ - 1}}a

  10. Co{s^{ - 1}}a = Ta{n^{ - 1}}\left(       {\frac{{\sqrt {1 - {a^2}} }}{a}} \right){\text{ }}0 < a \leqslant 1

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