cosec(cos^-1 (1/y)

Jun 2008
175
2
Can someone please check this for me thanks.

Question is \(\displaystyle \cos ec(\cos ^{ - 1} (\frac{1}{y})) = \)


This is what I worked it to be
\(\displaystyle
\begin{array}{l}
{\rm let }\theta = \cos ^{ - 1} (\frac{1}{y}) \\
\cos \theta = \frac{1}{y} \\
\cos ^2 \theta + \sin ^2 \theta = 1 \\
(\frac{1}{y})^2 + \sin ^2 \theta = 1 \\
\sin ^2 \theta = 1 - (\frac{1}{y})^2 \\
\sin \theta = \sqrt {1 - \left( {\frac{1}{y}} \right)^2 } \\
\cos ec\theta = \frac{1}{{\sin \theta }} = \frac{1}{{\sqrt {1 - \left( {\frac{1}{y}} \right)^2 } }} \\
\end{array}
\)

Is it right?(Thinking)
 
Sep 2006
782
100
The raggedy edge.
I did it a similar way and got what you did in a different form:



My working was virtually the same.
 
Last edited:
Jun 2008
175
2
not sure how to get from what I go to what you have ie y/(y+1)(y-1)