Question

Напишите подробное доказательство!!! Очень нужно!!!!

Answer 1

(tgα+ctgα)*(1-cos(4α)=
=(sinα/cosα+cosα/sinα)*(sin²(2α)+cos²(2α)-cos²(2α)+sin²(2α))=
=((sin²α+cos²α)/(sinα*cosα))*2*sin²(2α)=
=(1/(sinα*cosα))*2*sin²(2α)=(2/(2*sinα*cosα))*2*sin²(2α)=
=4*sin²(2α)/sin(2α)≡4*sin(2α).