Trigonometric Proof
Prove sinu + sinv = 2sin (u+v/2) cos (uv/2)
1. 2sin (u+v/2) cos (uv/2)

1. Given

2. sinu cosv = ½ (sin (u+v) + sin (uv))

2. This is the producttosum formula,
½ (sin (u+v) + sin (uv)) that was also given. 
3. 2 x ½ (sin (u+v – (uv)/s) + sin (u+v+uv)/2)

3. Plug in the equation 2sin (u+v/2) cos (uv/2)

4. 1 (sin (2v/2) + sin (2u/2))

4. Distributive property of multiplication and combine like terms.

5. 1 (sinv + sinu) = sinv + sinu

5. Simplify!

Paragraph Proofs: I would like to prove that sinu + sinv = 2sin (u+v/2) cos (uv/2). I was given that sinu cosv = ½ (sin (u+v) + sin (uv)) so I plugged 2sin (u+v/2) cos (uv/2) into ½ (sin (u+v) + sin (uv)) and I got 2 x ½ (sin (u+v – (uv)/s) + sin (u+v+uv)/2). Then I used the distributive property of multiplication and combined like terms to get 1 (sin (2v/2) + sin (2u/2)) and lastly, I simplified the equation to get sinv + sinu.
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