trigonometric integrals

**genlovesmusic09** · October 4th 2009, 01:19 PM

${\sec ^2}({\cos ^{ - 1}}(1 - x))<br />$
I'm not sure where to begin.

**DeMath** · October 4th 2009, 01:33 PM

Originally Posted by genlovesmusic09

${\sec ^2}({\cos ^{ - 1}}(1 - x))<br />$
I'm not sure where to begin.

First, simplifying

${\color{red}\boxed{\color{black}{\cos {{\cos }^{ - 1}}\theta = \cos \arccos \theta = \theta }}}$

${\sec ^2}{\cos ^{ - 1}}\left( {x - 1} \right) = {\left( {\frac{1}{{\cos {{\cos }^{ - 1}}\left( {x - 1} \right)}}} \right)^2} = {\left( {\frac{1}{{x - 1}}} \right)^2} = \frac{1}{{{{\left( {x - 1} \right)}^2}}}.$

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