Ответы на вопрос:
sin(45°+α)+cos(45°+α)]/[sin(45°+α)-cos(45°+α)]=
=[sin(45°+α)+cos(45°+α)]²/[sin(45°+α)²-cos(45°+α)²]=
=[sin²(45°+α)+2sin(45°+α)cos(45°+α)+cos²(45°+α)]/[-cos(90°+2α)]=
=[1+sin(90°+2α)]/sin2α=(1+cos2α)/sin2α=
=2cos²α/2sinαcosα=cosα/sinα=tgα;
используемые формулы:
1.(a+b)/(a-b)=(a+b)²/(a-b)(a+b)=(a+b)²/(a²-b²);
2.(a+b)²=a²+2ab+b²;
3.sin²α+cos²α=1;
4.2sinαcosα=sin2α;
5.cos²α-sin²α=cos2α;
6.sin(90°+α)=cosα;cos(90°+α)=-sinα;
7.sinα/cosα=tgα;
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