SOLUTION: Sinx-cosx+1/sinx+cosx-1

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Question 983144: Sinx-cosx+1/sinx+cosx-1
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You might really mean this: (Sin(x)-cos(x)+1)/(sin(x)+cos(x)-1)
when the correct grouping parentheses are used.

highlight_green%28%28Sin%28x%29-cos%28x%29%2B1%29%2F%28sin%28x%29%2Bcos%28x%29-1%29%29

%28Sin%28x%29-cos%28x%29%2B1%29%2F%28sin%28x%29%2Bcos%28x%29-1%29
%28sin%28x%29-%28cos%28x%29-1%29%29%2F%28sin%28x%29%2B%28cos%28x%29-1%29%29

This trick will let you take advantage of resulting difference of squares:

Difficulty managing the text and symbols, but the attempt is multiply expression by the factor %28sin%28x%29-%28cos%28x%29-1%29%29%2F%28sin%28x%29-%28cos%28x%29-1%29%29=1.

Continuing,...






skipping a step,
%281-2sin%28x%29cos%28x%29%2B1%29%2F%281-cos%5E2%28x%29-cos%5E2%28x%29%2B2cos%28x%29-1%29

%28-2sin%28x%29cos%28x%29%29%2F%28-2cos%5E2%28x%29%2B2cos%28x%29%29

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

and then cancel 1=cos%28x%29%2Fcos%28x%29

highlight%28sin%28x%29%2F%28cos%28x%29%2B1%29%29, and you might be able to do a little more with this.