Interal Explenation: Sec^3 to Cos Conversion

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Stratosphere
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This isn't a homework question so I decided not to post it there, can someone quickly explain what happened here,
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I can't figure out how they got the sec[tex]^{3}[/tex] into sec and then how they got sec into cos it doesn't explain anything on the website either.
 

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Um, they canceled sec^2(theta) from the top and bottom? And also the definition of sec is 1/cos...
 
Yeah I realized that they canceled sec^2 after I posted it. I get now why the changed sec^-1 to cos thanks, I guess I forgot some of my trig.