SOLUTION: how do you prove that sinxCosx=cosx-cos^3x/sinx are egual? also 2+2Cot^2= 2cotx secx cscx?

Algebra ->  Trigonometry-basics -> SOLUTION: how do you prove that sinxCosx=cosx-cos^3x/sinx are egual? also 2+2Cot^2= 2cotx secx cscx?      Log On


   

Question 370078: how do you prove that sinxCosx=cosx-cos^3x/sinx are egual?
also 2+2Cot^2= 2cotx secx cscx?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let S=sin%28x%29,C=cos%28x%29 to reduce some of the clutter,
.
.
S%5E2%2BC%5E2=1
S%5E2C%2BC%5E3=C
S%5E2C=C-C%5E3
SC=%28C-C%5E3%29%2FS
Now just go backwards.
.
.
.
S%5E2%2BC%5E2=1
1%2BC%5E2%2FS%5E2=1%2FS%5E2
2%281%2BC%5E2%2FS%5E2%29=2%2FS%5E2
2%281%2BC%5E2%2FS%5E2%29=2%281%2FS%5E2%29%28C%2FC%29
2%281%2BC%5E2%2FS%5E2%29=2%28C%2FS%29%281%2FC%29%281%2FS%29
2%2B2%28C%5E2%2FS%5E2%29=2%28C%2FS%29%281%2FC%29%281%2FS%29
Again work backwards.