cosec(cos^-1 (1/y)

**Craka** · September 11th 2008, 04:10 AM

Can someone please check this for me thanks.

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

This is what I worked it to be
$ \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?

**Showcase_22** · September 11th 2008, 04:32 AM

I did it a similar way and got what you did in a different form:

My working was virtually the same.

**Craka** · September 11th 2008, 05:05 AM

not sure how to get from what I go to what you have ie y/(y+1)(y-1)

**Showcase_22** · September 11th 2008, 05:11 AM

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