Question

Sin(4a-5π/6)+sin(4a-π/6)=

Answer 1

Ответ:

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Answer 2

To simplify the expression Sin(4a-5π/6)+sin(4a-π/6), we can use the sum-to-product trigonometric identities. The identity states that sin(x) + sin(y) = 2sin((x+y)/2)cos((x-y)/2). Applying this identity, we have:

Sin(4a-5π/6)+sin(4a-π/6) = 2sin((4a-5π/6 + 4a-π/6)/2)cos((4a-5π/6 - 4a+π/6)/2) = 2sin((8a - 6π/6)/2)cos((3π/6)/2) = 2sin((8a - π)/2)cos(π/6) = 2sin(4a - π)cos(π/6)

Therefore, the simplified expression is 2sin(4a - π)cos(π/6).