1. 1/(1-tgα)=1/(1-(sinα/cosα))=1/((cosα-sinα)/cosα)=cosα/(cosα-sinα).
2. 1/(1+tgα)=1/(1+(sinα/cosα))=1/((cosα+sinα)/cosα)=cosα/(cosα+sinα).
3. (cosα/(cosα-sinα))-(cosα/(cosα+sinα))=
=(cosα(cosα+sinα)-cosα(cosα-sinα))/((cosα+sinα)*(cosα-sinα)=
=(cos²α+sinαcosα-cos²α+sinαcosα)/(cos²α-sin²α)=
=2*sinα*cosα/cos2α=sin2α/cos2α≡tg2α.
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1. 1/(1-tgα)=1/(1-(sinα/cosα))=1/((cosα-sinα)/cosα)=cosα/(cosα-sinα).
2. 1/(1+tgα)=1/(1+(sinα/cosα))=1/((cosα+sinα)/cosα)=cosα/(cosα+sinα).
3. (cosα/(cosα-sinα))-(cosα/(cosα+sinα))=
=(cosα(cosα+sinα)-cosα(cosα-sinα))/((cosα+sinα)*(cosα-sinα)=
=(cos²α+sinαcosα-cos²α+sinαcosα)/(cos²α-sin²α)=
=2*sinα*cosα/cos2α=sin2α/cos2α≡tg2α.