SOLUTION: Verify the identity. (cos(x) - cos(y))/(sin(x) + sin(y)) + (sin(x) - sin(y))/(cos(x) + cos(y)) = 0

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: Verify the identity. (cos(x) - cos(y))/(sin(x) + sin(y)) + (sin(x) - sin(y))/(cos(x) + cos(y)) = 0      Log On

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Question 140847: Verify the identity.
(cos(x) - cos(y))/(sin(x) + sin(y)) + (sin(x) - sin(y))/(cos(x) + cos(y)) = 0
Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
%28cos%28x%29+-+cos%28y%29%29%2F%28sin%28x%29+%2B+sin%28y%29%29+%2B+%28sin%28x%29+-+sin%28y%29%29%2F%28cos%28x%29+%2B+cos%28y%29%29+=+0

LCD is just the product of the denominators, so:
%28%28%28cos%28x%29+-+cos%28y%29%29%28cos%28x%29%2Bcos%28y%29%29%29+%2B+%28%28sin%28x%29+-+sin%28y%29%29%28sin%28x%29%2Bsin%28y%29%29%29%29%2F%28%28sin%28x%29%2Bsin%28y%29%29%28cos%28x%29+%2B+cos%28y%29%29%29+=+0

%28cos%5E2%28x%29-cos%5E2%28y%29%2Bsin%5E2%28x%29-sin%5E2%28y%29%29%2F%28%28sin%28x%29%2Bsin%28y%29%29%28cos%28x%29+%2B+cos%28y%29%29%29=0 (Difference of 2 squares)

%28cos%5E2%28x%29%2Bsin%5E2%28x%29-cos%5E2%28y%29-sin%5E2%28y%29%29%2F%28%28sin%28x%29%2Bsin%28y%29%29%28cos%28x%29+%2B+cos%28y%29%29%29=0

%28cos%5E2%28x%29%2Bsin%5E2%28x%29-%28cos%5E2%28y%29%2Bsin%5E2%28y%29%29%29%2F%28%28sin%28x%29%2Bsin%28y%29%29%28cos%28x%29+%2B+cos%28y%29%29%29=0

%281-1%29%2F%28%28sin%28x%29%2Bsin%28y%29%29%28cos%28x%29+%2B+cos%28y%29%29%29=0 (because cos%5E2%28alpha%29%2Bsin%5E2%28alpha%29=1)

0%2F%28%28sin%28x%29%2Bsin%28y%29%29%28cos%28x%29+%2B+cos%28y%29%29%29=0