Question

Докажите, пожалуйста, тождество и упростите выражение

Answer 1

COS(π-α)= - COS(α),   SIN(π/2-α)=COS(α),  SIN(2α)=2SIN(α)COS(α)

[SIN(2α)+COS(π-α)SIN(α)]/SIN(π/2-α)=[2SIN(α)COS(α)-COS(α)SIN(α)]/COS(α) = SIN(α)COS(α)/COS(α) = SIN(α)

2) COS(2α) / (SIN(α)-COS(α))↑2-SIN(2α)



COS(2α) = COS²(α) - SIN²(α) =  (COS(α) - SIN(α) )·(COS(α) + SIN(α) )


[COS(2α)/( SIN(α) - COS(α))]²-SIN(2α) =

=[ (COS(α) - SIN(α) )·(COS(α) + SIN(α) )/(SIN(α) -COS(α)) ]²-
-2COS(α) SIN(α)=
= COS²(α) + 2COS(α)SIN(α) +SIN²(α)-2COS(α) SIN(α)=
=COS²(α) +SIN²(α)=1