Tg(x - 5π/4) = -tg(5π/4 - x) = -tg(π + π/4 -x) = -tg(π/4-x)= -(1-tgx)/(1 +tgx)=
=-(Cosx - Sinx)/(Cosx +Sinx)
Sin²(x + 5π/4) = Sin²(π/4 +x)=(√2/2Cosx + √2/2 Sinx)²= 1/2*(Cosx +Sinx)²
сам пример теперь:
-(Cosx -Sinx)/(Cosx + Sinx) * (Cosx +Sinx)² = -(Cosx - Sinx)(Cosx +Sinx) =
-(Cos²x - Sin²x) = -Cos2x