SOLUTION: cos y/ 1-tan y+ (sin y/1-cot y)=sin y +cos y

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Question 998939: cos y/ 1-tan y+ (sin y/1-cot y)=sin y +cos y
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
cos y/ 1-tan y+ (sin y/1-cot y)=sin y +cos y

+cosy%2F%281-%28siny%2Fcosy%29%29+%2B+%28siny%2F%281-cosy%2Fsiny%29%29

cosy%2F%28%28cosy-siny%29%2Fcosy%29+%2B+%28siny%2F%28%28siny-cosy%29%2Fsiny%29%29


%28cos%5E2%28y%29%2F%28cosy-siny%29%29%2B+%28+sin%5E2%28y%29%2F%28siny-cosy%29%29


%28cos%5E2%28y%29%2F%28cosy-siny%29%29-+%28+sin%5E2%28y%29%29%2F%28cosy-siny%29%29

%28cos%5E2%28y%29-sin%5E2%28y%29%29%2F%28cosy-siny%29

%28%28cosy%2Bsiny%29%28cosy-siny%29%29%2F%28cosy-siny%29

=cosy +siny

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
%28cos%28y%29%29%2F%281-tan%28y%29%29 + %28sin%28y%29%29%2F%281-cot%28y%29%29 = %28cos%28y%29%29%2F%281+-+%28sin%28y%29%2F%28cos%28y%29%29%29%29 + %28sin%28y%29%29%2F%281+-+%28cos%28y%29%2F%28sin%28y%29%29%29%29 = %28cos%28y%29%29%2F%28%28%28cos%28y%29+-+sin%28y%29%29%2F%28cos%28y%29%29%29%29 + %28sin%28y%29%29%2F%28%28%28sin%28y%29+-+cos%28y%29%29%2F%28sin%28y%29%29%29%29 = %28cos%5E2%28y%29%29%2F%28cos%28y%29+-+sin%28y%29%29 + %28sin%5E2%28y%29%29%2F%28sin%28y%29+-+cos%28y%29%29 =

%28cos%5E2%28y%29%29%2F%28cos%28y%29+-+sin%28y%29%29 - %28sin%5E2%28y%29%29%2F%28cos%28y%29+-+sin%28y%29%29 = %28cos%5E2%28y%29+-+sin%5E2%28y%29%29%2F%28cos%28y%29+-+sin%28y%29%29 = = = cos(y) + sin(y).

It is what has to be proved.