Упростите выражение sin(α-π)·cos(3π/2+α)-ctg(α-π)·sin(π/2+α)·cos(π/2-α).

Question

Упростите выражение sin(α-π)·cos(3π/2+α)-ctg(α-π)·sin(π/2+α)·cos(π/2-α).

Answer 1

-sin(π-a)*cos(3π/2+a)-ctg(a-π)*sin(π/2+a)*cos(π/2-a)=
=-sina*sina-ctga*cosa*sina=-sin²a-cosa*cosa*sina/sina=
=-sin²a-cos²a=-(sin²a+cos²a)=-1