Sin (π/2- )(cos²(3π/2-α)+cos²(π+α)) / sin (2π-α)

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To simplify the expression, we can use trigonometric identities to manipulate the terms. We start by expanding the numerator:

cos²(3π/2 - α) + cos²(π + α)
= cos²(3π/2)cos²(α) + cos²(π)cos²(α) (using cosine difference identity)
= 0 + cos²(α)
= cos²(α)

Now we substitute this back into the numerator:

sin(π/2 - α) * cos²(α) / sin(2π - α)

Since sin(π/2 - α) = cos(α), the expression simplifies to:

cos(α) * cos²(α) / sin(2π - α)

Now, we can simplify further by using trigonometric identities such as the sine and cosine addition identities:

cos(α) * cos²(α) / sin(2π)cos(α) - cos(α)sin(2π)sin(α)

cos(α) * cos²(α) / 0 - 0 (since sin(2π) = 0 and cos(2π) = 1)

So, the simplified expression is:

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