# Verify that sin(A+B) + sin(A-B) = 2sinA sinB ?

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It is not an identity.

It is not an identity.

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To verify the identity sin(A+B) + sin(A-B) = 2sinA sinB, we'll start by expanding sin(A+B) and sin(A-B) using the sum and difference identities for sine:

sin(A+B) = sinA cosB + cosA sinB sin(A-B) = sinA cosB - cosA sinB

Now, let's add sin(A+B) and sin(A-B) together:

sin(A+B) + sin(A-B) = (sinA cosB + cosA sinB) + (sinA cosB - cosA sinB)

Grouping like terms:

= sinA cosB + sinA cosB + cosA sinB - cosA sinB

Simplify by combining the like terms:

= 2sinA cosB

Using the identity sin(2θ) = 2sinθ cosθ, where θ = A, we can rewrite 2sinA cosB as sin(2A):

= sin(2A)

So, sin(A+B) + sin(A-B) = sin(2A).

Therefore, the identity sin(A+B) + sin(A-B) = 2sinA sinB is not valid. The correct identity is sin(A+B) + sin(A-B) = 2sinA cosB.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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