Sin(-α)*sin(90+α)/cos(180-α)*cos(-α)

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вопрос

Let's simplify the given expression step by step:

sin(-α) = -sin(α) (due to the odd nature of the sine function)sin(90+α) = sin(90)cos(α) + cos(90)sin(α) = cos(α)cos(180-α) = -cos(α) (due to the even nature of the cosine function)cos(-α) = cos(α) (due to the even nature of the cosine function)

Substitute these values into the expression:

(-sin(α) cos(α))/(-cos(α) cos(α))

Now simplify further:

= -sin(α) cos(α) / -cos(α)^2
= sin(α) cos(α) / cos(α)^2
= sin(α) / cos(α)
= tan(α)

Therefore, the final simplified expression is tan(α).