Simplify (cosx)/(1-sinx)

Question

I can't figure out how to simplify this correctly. Thanks for your help.

Answer 1

Hi, Leah.

 

Remember that 1-sin²x = cos²x

 

So if you multiply this fraction (cosx)/(1-sinx) by (1+sinx)/(1+sinx) you will get:

(cosx)(1+sinx)/(1-sin²x) = (cosx)(1+sinx)/(cos²x) or (1+sinx)/(cosx)

 

or: 1/cosx + sinx/cosx = secx + tanx.

 

I hope this helps.

 

Kevin