= sin(π/2-α) - cos(π-α) + tan(π-α) - cot(3π/2+α)
Using trigonometric identities:
= cos α - sin α + tan(α) - cot(α - π)
= cos α - sin α + tan(α) + cot(α)
= cos α - sin α + sin α / cos α + cos α / sin α
= 2cos α
Therefore, the final simplified expression is 2cos α.
= sin(π/2-α) - cos(π-α) + tan(π-α) - cot(3π/2+α)
Using trigonometric identities:
= cos α - sin α + tan(α) - cot(α - π)
= cos α - sin α + tan(α) + cot(α)
= cos α - sin α + sin α / cos α + cos α / sin α
= 2cos α
Therefore, the final simplified expression is 2cos α.