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38.

sec^6(x)(sec(x)tan(x))-sec^4(x)(sec(x)tan(x))=sec^5(x)tan^3(x)

sec^6(x)(sec(x)tan(x))-sec^4(x)(sec(x)tan(x))

=sec^6(x)(sec(x)tan(x))-sec^4(x)(sec(x)tan(x))........tan(x)=sec(x)/csc(x)

=sec^6(x)(sec(x)(sec(x)/csc(x)))-sec^4(x)(sec(x)(sec(x)/csc(x)))

=sec^5(x)((sec^3(x)/csc(x)))-sec^5(x)((sec(x)/csc(x)))

=sec^5(x)((sec^3(x)/csc(x))-(sec(x)/csc(x)))

=sec^5(x)((sec^2(x)(sec(x)/csc(x))-(sec(x)/csc(x)))

=sec^5(x)((sec^2(x)tan(x)-tan(x)))

=sec^5(x)((sec^2(x)-1)tan(x))

=sec^5(x)tan^2(x)tan(x)

=sec^5(x)tan^3(x)

42. correct

[QUOTE="MathLover1, post: 1099211, member: 280"] 38. sec^6(x)(sec(x)tan(x))-sec^4(x)(sec(x)tan(x))=[B]sec^5(x)tan^3(x)[/B] sec^6(x)(sec(x)tan(x))-sec^4(x)(sec(x)tan(x)) =sec^6(x)(sec(x)tan(x))-sec^4(x)(sec(x)tan(x))........tan(x)=sec(x)/csc(x) =sec^6(x)(sec(x)(sec(x)/csc(x)))-sec^4(x)(sec(x)(sec(x)/csc(x))) =sec^5(x)((sec^3(x)/csc(x)))-sec^5(x)((sec(x)/csc(x))) =sec^5(x)((sec^3(x)/csc(x))-(sec(x)/csc(x))) =sec^5(x)((sec^2(x)(sec(x)/csc(x))-(sec(x)/csc(x))) =sec^5(x)((sec^2(x)tan(x)-tan(x))) =sec^5(x)((sec^2(x)-1)tan(x)) =sec^5(x)tan^2(x)tan(x) =[B]sec^5(x)tan^3(x) 42. correct[/B] [/QUOTE]