SOLUTION: This is proving a trigonometric equation. Verify cos(x))/(1-sin(x))=sec(x)+tan(x) All I can figure out is how to expand it somewhat to be cos(x)/(1-sin(x)=(1/cos(x))+(sin(x

Algebra ->  Trigonometry-basics -> SOLUTION: This is proving a trigonometric equation. Verify cos(x))/(1-sin(x))=sec(x)+tan(x) All I can figure out is how to expand it somewhat to be cos(x)/(1-sin(x)=(1/cos(x))+(sin(x      Log On


   

Question 307241: This is proving a trigonometric equation.
Verify cos(x))/(1-sin(x))=sec(x)+tan(x)
All I can figure out is how to expand it somewhat to be
cos(x)/(1-sin(x)=(1/cos(x))+(sin(x)/cos(x) I have no clue where to go now.
Please help.
Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... Start with the given equation.


We're only going to manipulate the left side.


... Multiply both numerator and denominator of the left side by


Think of of the last step as rationalizing the denominator.


... FOIL


... Distribute


... Replace with


... Break up the fraction.


... Cancel out like terms.


... Use the identities and


Since the two sides are identical, this verifies the identity.