SOLUTION: hi I have a question concerning identitiy problems I need to prove that: Sec^6(x)(sec(x)tan(x)) - sec^4(x)(sec(x)tan(x)) = sec^5(x)tan^3(x) I wrote these in the order they occur

Question 427299: hi I have a question concerning identitiy problems
I need to prove that:
Sec^6(x)(sec(x)tan(x)) - sec^4(x)(sec(x)tan(x)) = sec^5(x)tan^3(x)
I wrote these in the order they occur in the book. I understand some write exponents as sec(x)^2.
If you can help, it would be greatly appreciated. Also, if you could show the work it would help very much because I don't exactly understand how to do these. Thank you!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
I need to prove that:
Sec^6(x)(sec(x)tan(x)) - sec^4(x)(sec(x)tan(x)) = sec^5(x)tan^3(x)
I need to prove that:
Sec^6(x)(sec(x)tan(x)) - sec^5(x)tan^3(x) - sec^4(x)(sec(x)tan(x)) = 0
Sec^2(x)(sec(x)tan(x)) - sec(x)tan^3(x) - (sec(x)tan(x)) = 0
Sec^2(x)(sec(x)) - sec(x)tan^2(x) - (sec(x)) = 0
Sec^2(x) - tan^2(x) - 1 = 0
1 -sin^2(x) - cos^2(x) = 0
sin^2 + cos^2 = 1
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