Maths > Inverse Trigonometric Function > 3.0 Properties
Inverse Trigonometric Function
1.0 Introduction
2.0 Inverse Trigonometric function
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
3.0 Properties
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
3.8 Property 8
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
3.2 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) ${\cos ^{ - 1}}x + {\cos ^{ - 1}}y$
\[ = \left\{ {\begin{array}{c} {{{\cos }^{ - 1}}\left\{ {xy - \sqrt {1 - {x^2}} \sqrt {1 - {y^2}} } \right\}}&{x,y \in [0,1]} \end{array}} \right.\]
(ii) ${\cos ^{ - 1}}x - {\cos ^{ - 1}}y$
\[ = \left\{ {\begin{array}{c} {{{\cos }^{ - 1}}\left\{ {xy + \sqrt {1 - {x^2}} \sqrt {1 - {y^2}} } \right\}}&{0 \leqslant x < y \leqslant 1} \\ { - {{\cos }^{ - 1}}\{ xy + \sqrt {1 - {x^2}} \sqrt {1 - {y^2}} }&{0 \leqslant y < x \leqslant 1} \end{array}} \right.\]
