SOLUTION: how do you simplify 1+sinx(-sinx)-cosx(cosx)/(1+sinx)^2

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Question 717569: how do you simplify 1+sinx(-sinx)-cosx(cosx)/(1+sinx)^2
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
How much of "1+sinx(-sinx)-cosx(cosx)" is in the numerator of the fraction? Please put numerators and denominators in parentheses to make it clear. Clearly posted problems get quicker responses.

If by chance all of "1+sinx(-sinx)-cosx(cosx)" is in the numerator (IOW, the expression is just one big fraction) then the answer is 0. Here's how:
%281%2Bsin%28x%29%28-sin%28x%29%29-cos%28x%29%28cos%28x%29%29%29%2F%281%2Bsin%28x%29%29%5E2
Multiplying in the numerator:
%281-sin%5E2%28x%29-cos%5E2%28x%29%29%2F%281%2Bsinx%29%5E2
Since 1-sin%5E2%28x%29+=+cos%5E2%28x%29:
%28cos%5E2%28x%29-cos%5E2%28x%29%29%2F%281%2Bsinx%29%5E2
Subtracting:
%280%29%2F%281%2Bsinx%29%5E2
which equals 0.