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
3.12 Property 12
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
\[\begin{gathered} (i)2{\tan ^{ - 1}}x = \left\{ \begin{gathered} {\sin ^{ - 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right); - 1 \leqslant x \leqslant 1 \hspace{1em} \\ \pi - {\sin ^{ - 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right);x > 1 \hspace{1em} \\ - \pi - {\sin ^{ - 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right);x < - 1 \hspace{1em} \\ \end{gathered} \right\} \hspace{1em} \\ (ii)2{\tan ^{ - 1}}x = \left\{ \begin{gathered} {\cos ^{ - 1}}\left( {\frac{{1 - {x^2}}}{{1 + {x^2}}}} \right);0 \leqslant x \leqslant \infty \hspace{1em} \\ - {\cos ^{ - 1}}\left( {\frac{{1 - {x^2}}}{{1 + {x^2}}}} \right); - \infty \leqslant x \leqslant 0 \hspace{1em} \\ \end{gathered} \right\} \hspace{1em} \\ \end{gathered} \]
