SOLUTION: {{{sin(x)/(1+cos(x))=(1-cos(x))/sin(x)}}}

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Question 695154: sin%28x%29%2F%281%2Bcos%28x%29%29=%281-cos%28x%29%29%2Fsin%28x%29
Answer by pmatei(79) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28x%29%2F%281%2Bcos%28x%29%29=%281-cos%28x%29%29%2Fsin%28x%29
Because you deal with fractions you need to exclude from domain (possible answers) those values that will give you denominators equal to zero.
1%2Bcos%28x%29+=0
cos%28x%29=-1
x=pi
sin%28x%29=0
x=0 or x=pi or x=2%2Api
So for the interval [0,2%2Api] we cannot have as solutions 0, pi, or 2%2Api.
Now as you do with any proportion, multiply on diagonal (butterfly method):
%28sin%28x%29%29%5E2=%281-cos%28x%29%29%281%2Bcos%28x%29%29
%28sin%28x%29%29%5E2=1-%28cos%28x%29%29%5E2
%28sin%28x%29%29%5E2%2B%28cos%28x%29%29%5E2=1
1=1
So this relation is true for every allowed value in the interval.