Sin(a+π/8)*cos(a-π/24)

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вопрос

To simplify this expression, we will use the sum and difference formulas for sine and cosine.

Recall that:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

Let's apply these formulas to our expression:

sin(a + π/8) cos(a - π/24)
= (sin(a)cos(π/8) + cos(a)sin(π/8)) (cos(a)cos(π/24) + sin(a)sin(π/24))
= (sin(a)cos(π/8)cos(a)cos(π/24) + sin(a)cos(π/8)sin(a)sin(π/24) + cos(a)sin(π/8)cos(a)cos(π/24) + cos(a)sin(π/8)sin(a)sin(π/24))

Now we can distribute and simplify this expression further.