3.7 Property 7

2.1 ${\sin ^{ - 1}}x$:
2.2 ${\cos ^{ - 1}}x$:
2.3 ${\tan ^{ - 1}}x$:
2.4 ${\text{cose}}{{\text{c}}^{ - 1}}x$:
2.5 ${\sec^{ - 1}}x$
2.6 ${\cot^{ - 1}}x$
2.7 Summary

3.1 Property 1
3.2 Property 2
3.3 Property 3
3.4 Property 4
3.5 Property 5
3.6 Property 6
3.7 Property 7
3.8 Property 8
3.9 Property 9
3.10 Property 10
3.11 Property 11
3.12 Property 12
3.13 Property 13

(i) ${\sin ^{ - 1}}x + {\sin ^{ - 1}}y$

\[ = \left\{ {\begin{array}{c} {{{\sin }^{ - 1}}\left( {x\sqrt {1 - {y^2}} + y\sqrt {1 - {x^2}} } \right)}&{x \geqslant 0,y \geqslant 0,{x^2} + {y^2} \leqslant 1} \\ {\pi - {{\sin }^{ - 1}}\left( {x\sqrt {1 - {y^2}} + y\sqrt {1 - {x^2}} } \right)}&{x \geqslant 0,y \geqslant 0,{x^2} + {y^2} \geqslant 1} \end{array}} \right.\]

(ii) ${\sin ^{ - 1}}x - {\sin ^{ - 1}}y$

\[ = \left\{ {\begin{array}{c} {{{\sin }^{ - 1}}\left( {x\sqrt {1 - {y^2}} - y\sqrt {1 - {x^2}} } \right)}&{x,y \in [0,1]} \end{array}} \right.\]