i need to prove sinx-siny= 2 sin( (x - y)/2 ) cos( (x + y)/2 )

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- Nov 18th 2006, 04:11 PMlexmex1546proof
i need to prove sinx-siny= 2 sin( (x - y)/2 ) cos( (x + y)/2 )

- Nov 18th 2006, 05:22 PMputnam120
here is a simple say.

for some x and y.

after applying the sine addition and subtraction formulas,

, you will end up with

now note that we want this in terms of a and b so we have

and so using this we have

- Nov 19th 2006, 06:52 AMSoroban
Hello, lexmex1546!

This is a rehash of*putnam120*'s solution . . . with baby steps.

Quote:

Prove: .

We have these two formulas:

. .

. .

Subtract**(2)**from**(1)**: .

Let: .

Then**(3)**becomes: .