SOLUTION: simplify (1+sinx/cosx)+(cosx/1+sinx)

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Question 190769: simplify (1+sinx/cosx)+(cosx/1+sinx)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


%281%2BSinx%29%2FCosx+%2B+Cosx%2F%281%2BSinx%29

The LCD is Cosx%281%2BSinx%29

%28%281%2BSinx%29%281%2BSinx%29%2BCos%5E2x%29%2F%28Cosx%281%2BSinx%29%29

Multiply out the top:

%281%2B2Sinx%2BSin%5E2x%2BCos%5E2x%29%0D%0A%2F%28Cosx%281%2BSinx%29%29

Replace the Sin%5E2x%2BCos%5E2x by 1

%281%2B2Sinx%2B1%29%0D%0A%2F%28Cosx%281%2BSinx%29%29

Combine the 1 and 1 as 2.

%282%2B2Sinx%29%0D%0A%2F%28Cosx%281%2BSinx%29%29

Factor out 2 on the top:

%282%281%2BSinx%29%29%0D%0A%2F%28Cosx%281%2BSinx%29%29 

Cancel the %281%2BSinx%29's

%282%28cross%281%2BSinx%29%29%29%0D%0A%2F%28Cosx%28cross%281%2BSinx%29%29%29

2%2FCosx

You could quit here, but if you like
you can go further:

2%2A%281%2FCosx%29

Replace 1%2FCosx by Secx

2Secx

Edwin