Sin( 180-альфа)+cos(90+альфа)

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вопрос

Let's first simplify the expression by using the trigonometric identities:

sin(180-α) = sin(180)cos(α) - cos(180)sin(α) = 0(cos(α)) - (-1)(sin(α)) = sin(α)

cos(90+α) = cos(90)cos(α) - sin(90)sin(α) = 0(cos(α)) - 1(sin(α)) = -sin(α)

Now, we can substitute these values back into the expression:

sin(α) + (-sin(α)) = sin(α) - sin(α) = 0

Therefore, the simplified expression is 0.