SOLUTION: (sec(x)-cos(x))(csc(x)-sin(x))=tan(x)/1+tan^2(x) please prove the identity,. do only one side please & thank you!

Algebra ->  Triangles -> SOLUTION: (sec(x)-cos(x))(csc(x)-sin(x))=tan(x)/1+tan^2(x) please prove the identity,. do only one side please & thank you!      Log On


   

Question 924923: (sec(x)-cos(x))(csc(x)-sin(x))=tan(x)/1+tan^2(x) please prove the identity,. do only one side please & thank you!
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%28sec%28x%29%5E%22%22-cos%28x%29%29%28csc%28x%29%5E%22%22-sin%28x%29%29

sec%28x%29csc%28x%29-sec%28x%29sin%28x%29-cos%28x%29csc%28x%29%2Bcos%28x%29sin%28x%29





Get LCD:





%281-1%2Bcos%5E2%28x%29sin%5E2%28x%29%29%2F%28cos%28x%29sin%28x%29%29

%28cos%5E2%28x%29sin%5E2%28x%29%29%2F%28cos%28x%29sin%28x%29%29

cos%28x%29sin%28x%29

That is as simplified as we can get it, although
it does not look like the other side.

Even though you said to work with only one side of 
the identity, when we have simplified one side as 
much as possible and it still is not exactly like 
the other side, it is perfectly OK to then work 
with the other side to see if we can get it to 
this same simplified form.  So we will see if
we can get the other side to cos%28x%29sin%28x%29.

tan%28x%29%2F%281%2Btan%5E2%28x%29%29

tan%28x%29%2Fsec%5E2%28x%29

tan%28x%29%22%F7%22sec%5E2%28x%29

sin%28x%29%2Fcos%28x%29%22%F7%221%2Fcos%5E2%28x%29

sin%28x%29%2Fcos%28x%29%22%D7%22cos%5E2%28x%29%2F1

sin%28x%29cos%28x%29

cos%28x%29sin%28x%29

So we were able to get it to the same simplified
form.

In case you think this is a violation of
working with only one side, I'll be glad to
show that why it is not.  It is because those
last steps can be reversed and tacked onto
the first part and only the left side will
have been worked with.

Let me know if you are not satisfied with
working with only one side AT A TIME! 
I'll reverse those last steps and then you'll
see that it will be the same as only working 
with one side.  Your teacher should have 
pointed this out to you.

Edwin