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Math Help - trigonometric integrals

  1. #1
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    trigonometric integrals

    {\sec ^2}({\cos ^{ - 1}}(1 - x))<br />
    I'm not sure where to begin.
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  2. #2
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    Quote Originally Posted by genlovesmusic09 View Post
    {\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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