SOLUTION: Please solve this: Use the sum and difference identities to prove that: sin(x+y)-sin(x-y) = 2cosxsiny

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Question 1011263: Please solve this: Use the sum and difference identities to prove that:
sin(x+y)-sin(x-y) = 2cosxsiny
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

prove that:
sin%28x%2By%29-sin%28x-y%29+=+2cos%28x%29sin%28y%29+
by definition
sin+%28x+%2B+y%29++=+sin+%28x%29+cos%28y%29+%2B+cos+%28x%29+sin+%28y%29
sin+%28x+-y%29++=+sin+%28x%29+cos+%28y%29+-cos+%28x%29+sin%28y%29
so,




sin%28x%2By%29-sin%28x-y%29+=+cos+%28x%29+sin+%28y%29%2Bcos+%28x%29+sin%28y%29

sin%28x%2By%29-sin%28x-y%29+=+2cos+%28x%29+sin+%28y%29