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cos(x) / ( sec(x) - tan(x) ) 
= cos(x) / ( 1/cos(x) - sin(x)/cos(x) ) 
= cos² (x) / ( 1 - sin(x) ) 
= ( 1 - sin² (x) ) / ( 1 - sin(x) ) 
= ( 1 - sin(x) ) ( 1 + sin(x) ) / ( 1 - sin(x) ) 
= 1 + sin(x)

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