# How do you use the sum and difference identity to evaluate #sin((7pi)/12)#?

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To evaluate sin((7π)/12) using the sum and difference identity, we first express (7π)/12 as the sum or difference of angles whose sine values we know. In this case, we can rewrite (7π)/12 as (π/4) + (π/3). Then, we apply the sum identity for sine, which states that sin(A + B) = sinA * cosB + cosA * sinB. By substituting π/4 for A and π/3 for B, we can calculate sin((7π)/12) as sin(π/4) * cos(π/3) + cos(π/4) * sin(π/3). Simplifying these trigonometric functions gives us (√2/2) * (1/2) + (√2/2) * (√3/2). Further simplifying, we get (√2/4) + (√6/4), which equals (√2 + √6)/4. Therefore, sin((7π)/12) = (√2 + √6)/4.

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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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