Спростити вираз sin(45°+a) + cos(45°+a) / sin(45°+a) - cos(45°+a)​

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;