Verifying Trigonometric Identities...5

[nycmathguy]

Section 5.2

This is part 6 not 5.

 

[MathLover1]

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

 

[nycmathguy]

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

I had trouble with 38. When trigonometric identities have powers greater than 3, it's hard to break down the problem.

What about the link below?

Verifying Trigonometric Identities...4