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