Доказать тождество:
1) cos2a/(sina*cosa+sin^2a)= ctga -1;
2) (sin2a-2cosa)/sina-sin^2a)= -2ctga;
3) tga(1+cos2a)=sin2a;
4) ((1-cos2a+sin2a)/(cos2a+sin2a))*ctga=1;
1) cos2a/(sina*cosa+sin^2a)= ctga -1;
2) (sin2a-2cosa)/sina-sin^2a)= -2ctga;
3) tga(1+cos2a)=sin2a;
4) ((1-cos2a+sin2a)/(cos2a+sin2a))*ctga=1;
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Verified answer
1cos2a/(sina*cosa+sin^2a)= ctga -1
(cos²a-sin²a)/[sina(cosa+sina)=(cosa-sina)(cosa+sina)/[sina(cosa+sina)=
=(cosa-sina)/sina=cosa/sina-sina/sina=ctga-1
2
(sin2a-2cosa)/sina-sin^2a)= -2ctga
(2sinacosa-2cosa)/[sina(1-sina)]=2cosa(sina-1)/[sina(1-sina)]=
=-2cosa/sina=-2ctga
3
tga(1+cos2a)=sin2a
tga*2cos²a=sina*2cos²a/cosa=2sinacosa=sin2a