Sin(a+b)+sin(a-b)=2sin a * cos b

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To prove the trigonometric identity sin(a+b)+sin(a-b)=2sin a * cos b, we can use the trigonometric sum and difference identities.

Let's start with the left side of the identity:

sin(a+b) + sin(a-b)

Using the sum and difference identities for sine, we have:

sin(a)cos(b) + cos(a)sin(b) + sin(a)cos(b) - cos(a)sin(b)

Now, we can combine like terms:

sin(a)cos(b) + sin(a)cos(b) + cos(a)sin(b) - cos(a)sin(b)

This simplifies to:

2sin(a)cos(b)

Therefore, sin(a+b) + sin(a-b) = 2sin(a)cos(b), which verifies the trigonometric identity.