Question 969538: 1-sinx/cosx=cosx/1+sinx
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! NOTE:
I believe you meant  .
If that was not what you meant, then I solved the wrong problem.
You could write as
(1-sinx)/cosx=cosx/(1+sinx) , because
1-sin(x)/cos(x)= and cos(x)/1+sin(x)= .
The parentheses are implicit in .
The long horizontal line between numerator and denominator is a powerful grouping symbol that indicates that numerator and denominator must be calculated before doing the division.
When you cannot write two lines (as when you are entering calculations into a calculator or spreadsheet) you need to write the implicit parentheses.
The expressions in  do not exist (are undefined) when the denominators are zero.
 happens for  ,  , and all co-terminal angles.
In general, we could say that  for every integer 
makes and cannot be a solution to the equation above.
The values of  that make  <---> are
 and all co-terminal angles.
Those values will be excluded if we exclude for every integer
to make  .
As long as  for every integer ,
which makes and , we can multiply both sides of
times 
to get the equivalent equations
 ---> ---> ,
and since the last equation is a trigonometric identity,
true for all values of ,
the solution to is all values of ,
and the solution to
is all values of such that for every integer .
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